question_id stringlengths 22 24 | split stringclasses 3
values | domain stringclasses 1
value | task stringclasses 1
value | prompt stringlengths 308 354 | model_response stringlengths 368 700 | extracted_answer stringclasses 4
values | ground_truth stringclasses 2
values | correct bool 2
classes | finish_reason stringclasses 1
value | token_count int64 134 271 |
|---|---|---|---|---|---|---|---|---|---|---|
formal_logic_test_3000 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((Q → R) ∨ P ∧ Q))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((Q → R) ∨ P ∧ Q))
Given: P=True, Q=False, R=True
Step 1: List all subexpressions
e1 = Q = False
e2 = R = True
e3 = P = True
e4 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = False → True = True
e6 = e3 ∧ e4 = True ∧ False = False
Step 3: Evaluate ... | False | False | true | stop | 167 |
formal_logic_test_3001 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ R ∧ (P ∧ Q))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ R ∧ (P ∧ Q))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = R = True
e3 = P = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e3 ∧ e4 = True ∧ True = True
Step 3: Evaluate remaining
e6 = e2 ∧ e5 = True ∧ True = True... | True | True | true | stop | 150 |
formal_logic_test_3002 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ (Q ∨ R ∨ P ∧ P))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∨ (Q ∨ R ∨ P ∧ P))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = True
e3 = R = False
e4 = P = True
e5 = P = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e2 ∨ e3 = True ∨ False = True
e7 = e4 ∧ e5 = True ∧ True = True
St... | True | True | true | stop | 185 |
formal_logic_test_3003 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ (Q ∧ P) → R)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ (Q ∧ P) → R)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = Q = False
e3 = P = True
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ∧ e3 = False ∧ True = False
Step 3: Evaluate remaining
e6 = e1 ∧ e5 = True ∧ False... | True | True | true | stop | 151 |
formal_logic_test_3004 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q → R ∨ Q ↔ R) ∧ P)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q → R ∨ Q ↔ R) ∧ P)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = R = True
e3 = Q = True
e4 = R = True
e5 = P = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e2 ∨ e3 = True ∨ True = True
Step 3: Evaluate remaining
e7 = e1 → e6 ... | True | True | true | stop | 186 |
formal_logic_test_3005 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬Q → R ∧ P)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬Q → R ∧ P)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = R = True
e3 = P = True
Step 2: Evaluate negations
e4 = ¬Q = False
Step 3: Evaluate binary operations (bottom to top)
e5 = e2 ∧ e3 = True ∧ True = True
Step 4: Evaluate remaining
e6 = e4 →... | True | True | true | stop | 134 |
formal_logic_test_3006 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ (¬Q → P) ∧ R)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ (¬Q → P) ∧ R)
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = False
e3 = P = False
e4 = R = True
Step 2: Evaluate negations
e5 = ¬Q = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e5 → e3 = True → False = False
Step 4: Eva... | False | False | true | stop | 169 |
formal_logic_test_3007 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ ¬((R ∨ Q)))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ ¬((R ∨ Q)))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = R = False
e3 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e4 = e2 ∨ e3 = False ∨ True = True
Step 3: Evaluate remaining
e5 = ¬e4 = ¬True = False
Step 4: Evaluate remai... | False | False | true | stop | 141 |
formal_logic_test_3008 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ Q → (P ↔ R ∨ P))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ Q → (P ↔ R ∨ P))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = Q = True
e3 = P = True
e4 = R = False
e5 = P = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ∨ e2 = True ∨ True = True
e7 = e4 ∨ e5 = False ∨ True = True
Ste... | True | True | true | stop | 182 |
formal_logic_test_3009 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((Q ∨ R → (P ↔ R)))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬((Q ∨ R → (P ↔ R)))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = R = False
e3 = P = True
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∨ e2 = False ∨ False = False
e6 = e3 ↔ e4 = True ↔ False = False
Step 3: Evalu... | False | False | true | stop | 167 |
formal_logic_test_3010 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ Q → (P ↔ P))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ Q → (P ↔ P))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = P = True
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e3 ↔ e4 = True ↔ True = True
Step 3: Evaluate remaining
e6 = e2 → e5 = True → True = True... | True | True | true | stop | 150 |
formal_logic_test_3011 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((¬P ∨ (R → Q)) ∧ R)
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((¬P ∨ (R → Q)) ∧ R)
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = R = False
e3 = Q = False
e4 = R = False
Step 2: Evaluate negations
e5 = ¬P = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e2 → e3 = False → False = True
Step 4... | False | False | true | stop | 172 |
formal_logic_test_3012 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R → Q) ∧ (P ∨ Q) ↔ R)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant... | <think>
Problem: Evaluate ((R → Q) ∧ (P ∨ Q) ↔ R)
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = False
e3 = P = False
e4 = Q = False
e5 = R = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 → e2 = True → False = False
e7 = e3 ∨ e4 = False ∨ False = ... | False | False | true | stop | 181 |
formal_logic_test_3013 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ P ∧ (R → Q))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ P ∧ (R → Q))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = P = True
e3 = R = False
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = True ∧ True = True
e6 = e3 → e4 = False → True = True
Step 3: Evaluate remain... | True | True | true | stop | 143 |
formal_logic_test_3014 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((P ∨ (Q ∨ P ∨ R)))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬((P ∨ (Q ∨ P ∨ R)))
Given: P=True, Q=False, R=True
Step 1: List all subexpressions
e1 = P = True
e2 = Q = False
e3 = P = True
e4 = R = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ∨ e3 = False ∨ True = True
Step 3: Evaluate remaining
e6 = e5 ∨ e4 = True ∨ True ... | False | False | true | stop | 180 |
formal_logic_test_3015 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((R ↔ Q) → P ↔ Q))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((R ↔ Q) → P ↔ Q))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = P = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ↔ e2 = True ↔ True = True
Step 3: Evaluate remaining
e6 = e5 → e3 = True → True = T... | False | False | true | stop | 171 |
formal_logic_test_3016 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P → R ↔ P ↔ ¬Q)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P → R ↔ P ↔ ¬Q)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = R = False
e3 = P = True
e4 = Q = False
Step 2: Evaluate negations
e5 = ¬Q = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e1 → e2 = True → False = False
Step 4: Evalu... | False | False | true | stop | 167 |
formal_logic_test_3017 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R → P → R ∨ Q)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R → P → R ∨ Q)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = P = True
e3 = R = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = True → True = True
e6 = e3 ∨ e4 = True ∨ True = True
Step 3: Evaluate remaining
... | True | True | true | stop | 145 |
formal_logic_test_3018 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((R → Q)) ↔ Q ∨ P)
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬((R → Q)) ↔ Q ∨ P)
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = True
e3 = Q = True
e4 = P = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = False → True = True
e6 = e3 ∨ e4 = True ∨ False = True
Step 3: Evaluate ... | False | False | true | stop | 168 |
formal_logic_test_3019 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((Q ↔ R) ∧ R ∨ P))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((Q ↔ R) ∧ R ∨ P))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = R = True
e3 = R = True
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ↔ e2 = True ↔ True = True
Step 3: Evaluate remaining
e6 = e5 ∧ e3 = True ∧ True = T... | False | False | true | stop | 174 |
formal_logic_test_3020 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ (R → Q) ∨ ¬R)
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ (R → Q) ∨ ¬R)
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = R = False
e3 = Q = False
e4 = R = False
Step 2: Evaluate negations
e5 = ¬R = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e2 → e3 = False → False = True
Step 4: ... | True | True | true | stop | 175 |
formal_logic_test_3021 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P → (P ∨ R → Q))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P → (P ∨ R → Q))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = P = True
e3 = R = False
e4 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ∨ e3 = True ∨ False = True
Step 3: Evaluate remaining
e6 = e5 → e4 = True → False ... | False | False | true | stop | 153 |
formal_logic_test_3022 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((P ↔ R) ∧ (Q ↔ Q)))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((P ↔ R) ∧ (Q ↔ Q)))
Given: P=True, Q=False, R=True
Step 1: List all subexpressions
e1 = P = True
e2 = R = True
e3 = Q = False
e4 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ↔ e2 = True ↔ True = True
e6 = e3 ↔ e4 = False ↔ False = True
Step 3: Evaluate... | False | False | true | stop | 165 |
formal_logic_test_3023 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ (Q → R ↔ P))
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ (Q → R ↔ P))
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = True
e3 = R = False
e4 = P = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 → e3 = True → False = False
Step 3: Evaluate remaining
e6 = e5 ↔ e4 = False ↔ Fal... | False | False | true | stop | 150 |
formal_logic_test_3024 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ R ∨ ¬Q)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ R ∨ ¬Q)
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = R = True
e3 = Q = False
Step 2: Evaluate negations
e4 = ¬Q = True
Step 3: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = False ∧ True = False
Step 4: Evaluate remaining
e6 =... | True | True | true | stop | 137 |
formal_logic_test_3025 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ P ∧ Q ∨ (P → Q))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ P ∧ Q ∨ (P → Q))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = True
e3 = Q = True
e4 = P = True
e5 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e2 ∧ e3 = True ∧ True = True
e7 = e4 → e5 = True → True = True
Step... | False | False | true | stop | 179 |
formal_logic_test_3026 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ ((R → P) ∧ Q))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ ((R → P) ∧ Q))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = R = False
e3 = P = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 → e3 = False → True = True
Step 3: Evaluate remaining
e6 = e5 ∧ e4 = True ∧ True =... | True | True | true | stop | 151 |
formal_logic_test_3027 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R → P → Q ∨ R)
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R → P → Q ∨ R)
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = True
e3 = Q = True
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = False → True = True
e6 = e3 ∨ e4 = True ∨ False = True
Step 3: Evaluate remain... | True | True | true | stop | 145 |
formal_logic_test_3028 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R → P ↔ Q) → P)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R → P ↔ Q) → P)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = True
e3 = Q = False
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = False → True = True
Step 3: Evaluate remaining
e6 = e5 ↔ e3 = True ↔ False ... | True | True | true | stop | 150 |
formal_logic_test_3029 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∧ Q → P → R)
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∧ Q → P → R)
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = False
e3 = P = False
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = False ∧ False = False
Step 3: Evaluate remaining
e6 = e5 → e3 = False → Fa... | False | False | true | stop | 149 |
formal_logic_test_3030 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ↔ P → R ∧ Q)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ↔ P → R ∧ Q)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = P = True
e3 = R = False
e4 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e3 ∧ e4 = False ∧ False = False
Step 3: Evaluate remaining
e6 = e2 → e5 = True → False ... | False | False | true | stop | 149 |
formal_logic_test_3031 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q ↔ P) → Q ∨ R)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q ↔ P) → Q ∨ R)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = P = True
e3 = Q = False
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ↔ e2 = False ↔ True = False
e6 = e3 ∨ e4 = False ∨ False = False
Step 3: Evaluate... | True | True | true | stop | 146 |
formal_logic_test_3032 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∨ (Q ∨ R ∧ P) ∨ Q)
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q ∨ (Q ∨ R ∧ P) ∨ Q)
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = Q = True
e2 = Q = True
e3 = R = False
e4 = P = True
e5 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e3 ∧ e4 = False ∧ True = False
Step 3: Evaluate remaining
e7 = e2 ∨... | True | True | true | stop | 193 |
formal_logic_test_3033 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q → R ↔ (R ↔ P))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q → R ↔ (R ↔ P))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = R = False
e3 = R = False
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = False → False = True
e6 = e3 ↔ e4 = False ↔ True = False
Step 3: Evaluate ... | False | False | true | stop | 143 |
formal_logic_test_3034 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q → R ∨ ¬((P ↔ P)))
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q → R ∨ ¬((P ↔ P)))
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = R = True
e3 = P = False
e4 = P = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e3 ↔ e4 = False ↔ False = True
Step 3: Evaluate remaining
e6 = ¬e5 = ¬True = False
... | True | True | true | stop | 174 |
formal_logic_test_3035 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ R ∨ Q ∧ Q)
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ R ∨ Q ∧ Q)
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = R = True
e3 = Q = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = False ∧ True = False
e6 = e3 ∧ e4 = True ∧ True = True
Step 3: Evaluate remaini... | True | True | true | stop | 145 |
formal_logic_test_3036 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∧ P ∧ ¬((R ∨ Q)))
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∧ P ∧ ¬((R ∨ Q)))
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = P = False
e3 = R = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = True ∧ False = False
e6 = e3 ∨ e4 = True ∨ True = True
Step 3: Evaluate re... | False | False | true | stop | 167 |
formal_logic_test_3037 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ R → R → ¬Q)
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ R → R → ¬Q)
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = R = False
e3 = R = False
e4 = Q = False
Step 2: Evaluate negations
e5 = ¬Q = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e1 ∨ e2 = False ∨ False = False
Step 4: E... | True | True | true | stop | 170 |
formal_logic_test_3038 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ∨ ¬P → Q) ∨ R)
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R ∨ ¬P → Q) ∨ R)
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = False
e3 = Q = True
e4 = R = False
Step 2: Evaluate negations
e5 = ¬P = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e1 ∨ e5 = False ∨ True = True
Step 4: Eva... | True | True | true | stop | 174 |
formal_logic_test_3039 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∧ Q → (P → R))
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q ∧ Q → (P → R))
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = Q = False
e3 = P = False
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = False ∧ False = False
e6 = e3 → e4 = False → False = True
Step 3: Evalua... | True | True | true | stop | 143 |
formal_logic_test_3040 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∧ (P ↔ ¬Q ∧ R))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∧ (P ↔ ¬Q ∧ R))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = True
e3 = Q = False
e4 = R = False
Step 2: Evaluate negations
e5 = ¬Q = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e5 ∧ e4 = True ∧ False = False
Step 4: Ev... | False | False | true | stop | 168 |
formal_logic_test_3041 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((P → Q)) ∧ P ∧ R)
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬((P → Q)) ∧ P ∧ R)
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = Q = False
e3 = P = False
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = False → False = True
Step 3: Evaluate remaining
e6 = ¬e5 = ¬True = Fa... | False | False | true | stop | 172 |
formal_logic_test_3042 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q ∨ (P ↔ R)) ∧ P)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q ∨ (P ↔ R)) ∧ P)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = P = True
e3 = R = True
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ↔ e3 = True ↔ True = True
Step 3: Evaluate remaining
e6 = e1 ∨ e5 = True ∨ True = Tr... | True | True | true | stop | 154 |
formal_logic_test_3043 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ Q → (R ↔ R))
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ Q → (R ↔ R))
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = Q = True
e3 = R = True
e4 = R = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∨ e2 = False ∨ True = True
e6 = e3 ↔ e4 = True ↔ True = True
Step 3: Evaluate remain... | True | True | true | stop | 146 |
formal_logic_test_3044 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ (Q ∧ R ∨ (P ∨ P)))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ (Q ∧ R ∨ (P ∨ P)))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = P = True
e2 = Q = True
e3 = R = True
e4 = P = True
e5 = P = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e2 ∧ e3 = True ∧ True = True
e7 = e4 ∨ e5 = True ∨ True = True
Step... | True | True | true | stop | 186 |
formal_logic_test_3045 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P → Q ∧ P) ∧ (P ∨ R))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((P → Q ∧ P) ∧ (P ∨ R))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = P = True
e2 = Q = True
e3 = P = True
e4 = P = True
e5 = R = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e2 ∧ e3 = True ∧ True = True
e7 = e4 ∨ e5 = True ∨ True = True
Step... | True | True | true | stop | 180 |
formal_logic_test_3046 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ↔ ¬((P ∨ Q))) → P)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R ↔ ¬((P ∨ Q))) → P)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = P = True
e3 = Q = True
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ∨ e3 = True ∨ True = True
Step 3: Evaluate remaining
e6 = ¬e5 = ¬True = False
Ste... | True | True | true | stop | 175 |
formal_logic_test_3047 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∨ R → P ∨ Q)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q ∨ R → P ∨ Q)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = R = True
e3 = P = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∨ e2 = True ∨ True = True
e6 = e3 ∨ e4 = True ∨ True = True
Step 3: Evaluate remaining
... | True | True | true | stop | 148 |
formal_logic_test_3048 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬R ∨ (R → Q) ∧ P)
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬R ∨ (R → Q) ∧ P)
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = R = False
e3 = Q = True
e4 = P = False
Step 2: Evaluate negations
e5 = ¬R = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e2 → e3 = False → True = True
Step 4: Eva... | True | True | true | stop | 172 |
formal_logic_test_3049 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∧ ¬((¬P ∧ Q)))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∧ ¬((¬P ∧ Q)))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = P = True
e3 = Q = True
Step 2: Evaluate negations
e4 = ¬P = False
Step 3: Evaluate binary operations (bottom to top)
e5 = e4 ∧ e3 = False ∧ True = False
Step 4: Evaluate remaining
e6... | True | True | true | stop | 156 |
formal_logic_test_3050 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ (P ↔ Q) ∨ R)
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ (P ↔ Q) ∨ R)
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = P = True
e3 = Q = True
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ↔ e3 = True ↔ True = True
Step 3: Evaluate remaining
e6 = e1 ∨ e5 = True ∨ True = Tr... | True | True | true | stop | 157 |
formal_logic_test_3051 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ (R ∨ (Q ↔ P)))
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∨ (R ∨ (Q ↔ P)))
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = R = True
e3 = Q = False
e4 = P = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e3 ↔ e4 = False ↔ False = True
Step 3: Evaluate remaining
e6 = e2 ∨ e5 = True ∨ Tru... | True | True | true | stop | 157 |
formal_logic_test_3052 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ Q ∨ (P ∨ P ∨ R))
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∨ Q ∨ (P ∨ P ∨ R))
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = True
e3 = P = False
e4 = P = False
e5 = R = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ∨ e2 = False ∨ True = True
e7 = e3 ∨ e4 = False ∨ False = Fa... | True | True | true | stop | 188 |
formal_logic_test_3053 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ ((¬Q → R) ∨ P))
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∨ ((¬Q → R) ∨ P))
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = R = True
e4 = P = False
Step 2: Evaluate negations
e5 = ¬Q = False
Step 3: Evaluate binary operations (bottom to top)
e6 = e5 → e3 = False → True = True
Step 4: Eva... | True | True | true | stop | 175 |
formal_logic_test_3054 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R → Q ∨ (P ∨ R ∨ P))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R → Q ∨ (P ∨ R ∨ P))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = P = True
e4 = R = True
e5 = P = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e3 ∨ e4 = True ∨ True = True
Step 3: Evaluate remaining
e7 = e6 ∨ e5 ... | True | True | true | stop | 192 |
formal_logic_test_3055 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((¬P ∨ Q) ∧ R)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((¬P ∨ Q) ∧ R)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = P = True
e2 = Q = True
e3 = R = True
Step 2: Evaluate negations
e4 = ¬P = False
Step 3: Evaluate binary operations (bottom to top)
e5 = e4 ∨ e2 = False ∨ True = True
Step 4: Evaluate remaining
e6 = e... | True | True | true | stop | 138 |
formal_logic_test_3056 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬Q → (¬P ↔ R))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬Q → (¬P ↔ R))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = P = True
e3 = R = True
Step 2: Evaluate negations
e4 = ¬Q = False
e5 = ¬P = False
Step 3: Evaluate binary operations (bottom to top)
e6 = e5 ↔ e3 = False ↔ True = False
Step 4: Evaluat... | True | True | true | stop | 145 |
formal_logic_test_3057 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P → Q) ∧ ¬((P → R)))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((P → Q) ∧ ¬((P → R)))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = Q = False
e3 = P = True
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = True → False = False
e6 = e3 → e4 = True → False = False
Step 3: Evalu... | False | False | true | stop | 165 |
formal_logic_test_3058 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((R ∧ Q ∨ Q)) ∨ P)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬((R ∧ Q ∨ Q)) ∨ P)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = False
e3 = Q = False
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = False ∧ False = False
Step 3: Evaluate remaining
e6 = e5 ∨ e3 = False ∨... | True | True | true | stop | 178 |
formal_logic_test_3059 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P → Q ∧ Q → ¬R)
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P → Q ∧ Q → ¬R)
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = Q = True
e3 = Q = True
e4 = R = False
Step 2: Evaluate negations
e5 = ¬R = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e2 ∧ e3 = True ∧ True = True
Step 4: Evaluat... | True | True | true | stop | 167 |
formal_logic_test_3060 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((P ↔ Q) ∧ R))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((P ↔ Q) ∧ R))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = Q = False
e3 = R = False
Step 2: Evaluate binary operations (bottom to top)
e4 = e1 ↔ e2 = True ↔ False = False
Step 3: Evaluate remaining
e5 = e4 ∧ e3 = False ∧ False = False
Step 4:... | True | True | true | stop | 138 |
formal_logic_test_3061 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∧ ¬P ↔ Q ∧ R)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q ∧ ¬P ↔ Q ∧ R)
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = Q = False
e2 = P = False
e3 = Q = False
e4 = R = True
Step 2: Evaluate negations
e5 = ¬P = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e3 ∧ e4 = False ∧ True = False
Step 4: Eval... | True | True | true | stop | 167 |
formal_logic_test_3062 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ∨ Q ∨ (P ↔ R)) ∧ R)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R ∨ Q ∨ (P ↔ R)) ∧ R)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = P = True
e4 = R = True
e5 = R = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ∨ e2 = True ∨ True = True
e7 = e3 ↔ e4 = True ↔ True = True
Step... | True | True | true | stop | 183 |
formal_logic_test_3063 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ↔ Q) ∧ P ↔ R ∧ Q)
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R ↔ Q) ∧ P ↔ R ∧ Q)
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = P = False
e4 = R = True
e5 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ↔ e2 = True ↔ True = True
e7 = e4 ∧ e5 = True ∧ True = True
Step... | False | False | true | stop | 176 |
formal_logic_test_3064 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P ∨ ¬Q) ∧ (R ∧ Q))
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((P ∨ ¬Q) ∧ (R ∧ Q))
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = Q = True
e3 = R = False
e4 = Q = True
Step 2: Evaluate negations
e5 = ¬Q = False
Step 3: Evaluate binary operations (bottom to top)
e6 = e3 ∧ e4 = False ∧ True = False
Step 4: ... | False | False | true | stop | 172 |
formal_logic_test_3065 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ P ∨ R ∨ (R → Q))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∨ P ∨ R ∨ (R → Q))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = True
e3 = R = False
e4 = R = False
e5 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ∨ e2 = False ∨ True = True
e7 = e4 → e5 = False → True = True
... | True | True | true | stop | 185 |
formal_logic_test_3066 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ R ↔ Q ∨ P)
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∨ R ↔ Q ∨ P)
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = R = False
e3 = Q = True
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∨ e2 = False ∨ False = False
e6 = e3 ∨ e4 = True ∨ True = True
Step 3: Evaluate remai... | False | False | true | stop | 148 |
formal_logic_test_3067 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R → ¬((Q ∧ P)))
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R → ¬((Q ∧ P)))
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = P = False
Step 2: Evaluate binary operations (bottom to top)
e4 = e2 ∧ e3 = True ∧ False = False
Step 3: Evaluate remaining
e5 = ¬e4 = ¬False = True
Step 4: Evaluate rema... | True | True | true | stop | 138 |
formal_logic_test_3068 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((P ∨ Q → R) ∨ Q))
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((P ∨ Q → R) ∨ Q))
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = Q = False
e3 = R = True
e4 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∨ e2 = False ∨ False = False
Step 3: Evaluate remaining
e6 = e5 → e3 = False →... | False | False | true | stop | 177 |
formal_logic_test_3069 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬P ∧ Q ∧ (R ∨ P))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬P ∧ Q ∧ (R ∨ P))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = Q = False
e3 = R = False
e4 = P = True
Step 2: Evaluate negations
e5 = ¬P = False
Step 3: Evaluate binary operations (bottom to top)
e6 = e3 ∨ e4 = False ∨ True = True
Step 4: Eva... | False | False | true | stop | 171 |
formal_logic_test_3070 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((P ∧ Q)) ∨ R)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬((P ∧ Q)) ∨ R)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = P = True
e2 = Q = False
e3 = R = False
Step 2: Evaluate binary operations (bottom to top)
e4 = e1 ∧ e2 = True ∧ False = False
Step 3: Evaluate remaining
e5 = ¬e4 = ¬False = True
Step 4: Evaluate re... | True | True | true | stop | 142 |
formal_logic_test_3071 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((Q ∧ ¬R ∧ P))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬((Q ∧ ¬R ∧ P))
Given: P=True, Q=False, R=True
Step 1: List all subexpressions
e1 = Q = False
e2 = R = True
e3 = P = True
Step 2: Evaluate negations
e4 = ¬R = False
Step 3: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e4 = False ∧ False = False
Step 4: Evaluate remaining
e... | True | True | true | stop | 155 |
formal_logic_test_3072 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∧ (P ∨ R → Q))
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∧ (P ∨ R → Q))
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = P = False
e3 = R = True
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ∨ e3 = False ∨ True = True
Step 3: Evaluate remaining
e6 = e5 → e4 = True → True = T... | True | True | true | stop | 153 |
formal_logic_test_3073 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((R → Q)) ∧ ¬P)
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬((R → Q)) ∧ ¬P)
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = True
e3 = P = True
Step 2: Evaluate negations
e4 = ¬P = False
Step 3: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = False → True = True
Step 4: Evaluate remaining
e... | False | False | true | stop | 157 |
formal_logic_test_3074 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ (R → (Q → R)))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ (R → (Q → R)))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = P = True
e2 = R = True
e3 = Q = True
e4 = R = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e3 → e4 = True → True = True
Step 3: Evaluate remaining
e6 = e2 → e5 = True → True = Tr... | True | True | true | stop | 151 |
formal_logic_test_3075 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((Q ∧ R)) ∨ (R ∨ P))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬((Q ∧ R)) ∨ (R ∨ P))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = R = False
e3 = R = False
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = False ∧ False = False
e6 = e3 ∨ e4 = False ∨ True = True
Step 3: Eval... | True | True | true | stop | 172 |
formal_logic_test_3076 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P ∨ R → Q) ∧ (Q ∨ P))
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant... | <think>
Problem: Evaluate ((P ∨ R → Q) ∧ (Q ∨ P))
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = R = True
e3 = Q = False
e4 = Q = False
e5 = P = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ∨ e2 = False ∨ True = True
e7 = e4 ∨ e5 = False ∨ False = ... | False | False | true | stop | 183 |
formal_logic_test_3077 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R → (P → Q → ¬R))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R → (P → Q → ¬R))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = True
e3 = Q = False
e4 = R = False
Step 2: Evaluate negations
e5 = ¬R = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e2 → e3 = True → False = False
Step 4: Ev... | True | True | true | stop | 168 |
formal_logic_test_3078 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∨ (R → P ∧ R))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q ∨ (R → P ∧ R))
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = Q = True
e2 = R = False
e3 = P = True
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e3 ∧ e4 = True ∧ False = False
Step 3: Evaluate remaining
e6 = e2 → e5 = False → False... | True | True | true | stop | 153 |
formal_logic_test_3079 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q ↔ R) → (Q ↔ P ∧ P))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q ↔ R) → (Q ↔ P ∧ P))
Given: P=True, Q=False, R=True
Step 1: List all subexpressions
e1 = Q = False
e2 = R = True
e3 = Q = False
e4 = P = True
e5 = P = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ↔ e2 = False ↔ True = False
e7 = e4 ∧ e5 = True ∧ True = True... | True | True | true | stop | 177 |
formal_logic_test_3080 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((R ∨ Q ∨ (P ∨ P)))
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬((R ∨ Q ∨ (P ∨ P)))
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = P = False
e4 = P = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∨ e2 = True ∨ True = True
e6 = e3 ∨ e4 = False ∨ False = False
Step 3: Evaluate ... | False | False | true | stop | 173 |
formal_logic_test_3081 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P ∧ R → P) ∨ Q)
Given: P=False, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((P ∧ R → P) ∨ Q)
Given: P=False, Q=True, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = R = True
e3 = P = False
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∧ e2 = False ∧ True = False
Step 3: Evaluate remaining
e6 = e5 → e3 = False → False... | True | True | true | stop | 153 |
formal_logic_test_3082 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∧ ((P ↔ R) → P))
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q ∧ ((P ↔ R) → P))
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = P = False
e3 = R = False
e4 = P = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ↔ e3 = False ↔ False = True
Step 3: Evaluate remaining
e6 = e5 → e4 = True → ... | False | False | true | stop | 151 |
formal_logic_test_3083 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ R ∨ (Q → P → P))
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ R ∨ (Q → P → P))
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = R = True
e3 = Q = False
e4 = P = False
e5 = P = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ∧ e2 = False ∧ True = False
e7 = e3 → e4 = False → False = T... | False | False | true | stop | 179 |
formal_logic_test_3084 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ (P ↔ P) → Q)
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ (P ↔ P) → Q)
Given: P=False, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = False
e3 = P = False
e4 = Q = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ↔ e3 = False ↔ False = True
Step 3: Evaluate remaining
e6 = e5 → e4 = True → True... | False | False | true | stop | 151 |
formal_logic_test_3085 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ↔ (P ∧ R → Q) ∧ R)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ↔ (P ∧ R → Q) ∧ R)
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = P = False
e2 = P = False
e3 = R = True
e4 = Q = False
e5 = R = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e2 ∧ e3 = False ∧ True = False
Step 3: Evaluate remaining
e7 = e... | False | False | true | stop | 184 |
formal_logic_test_3086 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ↔ (P → R ↔ ¬P))
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (Q ↔ (P → R ↔ ¬P))
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = Q = False
e2 = P = False
e3 = R = True
e4 = P = False
Step 2: Evaluate negations
e5 = ¬P = True
Step 3: Evaluate binary operations (bottom to top)
e6 = e2 → e3 = False → True = True
Step 4: Eva... | False | False | true | stop | 168 |
formal_logic_test_3087 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q → Q) ∨ (R ↔ P → Q))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant... | <think>
Problem: Evaluate ((Q → Q) ∨ (R ↔ P → Q))
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = Q = False
e3 = R = False
e4 = P = True
e5 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 → e2 = False → False = True
e7 = e4 → e5 = True → False = ... | True | True | true | stop | 180 |
formal_logic_test_3088 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P ↔ (P → R ↔ Q)) ∧ R)
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistan... | <think>
Problem: Evaluate ((P ↔ (P → R ↔ Q)) ∧ R)
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = P = False
e3 = R = False
e4 = Q = False
e5 = R = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e2 → e3 = False → False = True
Step 3: Evaluate remaining
e... | False | False | true | stop | 184 |
formal_logic_test_3089 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ↔ Q) ∨ (P ∨ R) ∧ Q)
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R ↔ Q) ∨ (P ∨ R) ∧ Q)
Given: P=True, Q=False, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = False
e3 = P = True
e4 = R = True
e5 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ↔ e2 = True ↔ False = False
e7 = e3 ∨ e4 = True ∨ True = True... | False | False | true | stop | 184 |
formal_logic_test_3090 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q ↔ R) → ¬P)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q ↔ R) → ¬P)
Given: P=True, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = R = False
e3 = P = True
Step 2: Evaluate negations
e4 = ¬P = False
Step 3: Evaluate binary operations (bottom to top)
e5 = e1 ↔ e2 = False ↔ False = True
Step 4: Evaluate remaining
e... | False | False | true | stop | 135 |
formal_logic_test_3091 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ↔ P) ∨ P ∧ (R ∧ Q))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R ↔ P) ∨ P ∧ (R ∧ Q))
Given: P=True, Q=False, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = P = True
e3 = P = True
e4 = R = True
e5 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ↔ e2 = True ↔ True = True
e7 = e4 ∧ e5 = True ∧ False = False
... | True | True | true | stop | 180 |
formal_logic_test_3092 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q ↔ P) → P ↔ R ∨ R)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q ↔ P) → P ↔ R ∨ R)
Given: P=False, Q=False, R=True
Step 1: List all subexpressions
e1 = Q = False
e2 = P = False
e3 = P = False
e4 = R = True
e5 = R = True
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 ↔ e2 = False ↔ False = True
e7 = e4 ∨ e5 = True ∨ True = True... | False | False | true | stop | 179 |
formal_logic_test_3093 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ ¬((Q → R)))
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ ¬((Q → R)))
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = Q = False
e3 = R = False
Step 2: Evaluate binary operations (bottom to top)
e4 = e2 → e3 = False → False = True
Step 3: Evaluate remaining
e5 = ¬e4 = ¬True = False
Step 4: Evaluate ... | False | False | true | stop | 141 |
formal_logic_test_3094 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R → Q) ∧ (R → P))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R → Q) ∧ (R → P))
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = R = True
e2 = Q = True
e3 = R = True
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 → e2 = True → True = True
e6 = e3 → e4 = True → True = True
Step 3: Evaluate remaini... | True | True | true | stop | 144 |
formal_logic_test_3095 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ∨ Q ↔ P) ∧ R)
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((R ∨ Q ↔ P) ∧ R)
Given: P=True, Q=True, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = Q = True
e3 = P = True
e4 = R = False
Step 2: Evaluate binary operations (bottom to top)
e5 = e1 ∨ e2 = False ∨ True = True
Step 3: Evaluate remaining
e6 = e5 ↔ e3 = True ↔ True = ... | False | False | true | stop | 153 |
formal_logic_test_3096 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∨ (R ∨ (P ∨ P) ∧ Q))
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistan... | <think>
Problem: Evaluate (Q ∨ (R ∨ (P ∨ P) ∧ Q))
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = Q = False
e2 = R = False
e3 = P = False
e4 = P = False
e5 = Q = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e3 ∨ e4 = False ∨ False = False
Step 3: Evaluate remaining
... | False | False | true | stop | 194 |
formal_logic_test_3097 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P → Q ↔ R ∨ (Q ↔ P))
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P → Q ↔ R ∨ (Q ↔ P))
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = P = False
e2 = Q = False
e3 = R = False
e4 = Q = False
e5 = P = False
Step 2: Evaluate binary operations (bottom to top)
e6 = e1 → e2 = False → False = True
e7 = e4 ↔ e5 = False ↔ False =... | True | True | true | stop | 179 |
formal_logic_test_3098 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q → R ∧ Q) ∧ P)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q → R ∧ Q) ∧ P)
Given: P=True, Q=True, R=True
Step 1: List all subexpressions
e1 = Q = True
e2 = R = True
e3 = Q = True
e4 = P = True
Step 2: Evaluate binary operations (bottom to top)
e5 = e2 ∧ e3 = True ∧ True = True
Step 3: Evaluate remaining
e6 = e1 → e5 = True → True = True... | True | True | true | stop | 150 |
formal_logic_test_3099 | test | formal_logic | formal_logic_truth_table | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬(¬R) ∨ (P ∨ Q))
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬(¬R) ∨ (P ∨ Q))
Given: P=False, Q=False, R=False
Step 1: List all subexpressions
e1 = R = False
e2 = P = False
e3 = Q = False
Step 2: Evaluate negations
e4 = ¬R = True
Step 3: Evaluate binary operations (bottom to top)
e5 = e2 ∨ e3 = False ∨ False = False
Step 4: Evaluate remainin... | False | False | true | stop | 164 |
End of preview. Expand in Data Studio
algo-sft-eval-traces-formal-logic-truth-table-v4
Full eval traces for algo-sft-formal-logic-truth-table across test/harder/ood splits
Dataset Info
- Rows: 2000
- Columns: 11
Columns
| Column | Type | Description |
|---|---|---|
| question_id | Value('string') | Unique question identifier from eval set |
| split | Value('string') | Evaluation split: test (in-distribution), harder (scaled up), ood (structural out-of-distribution) |
| domain | Value('string') | Task domain: formal_logic, conlang_morphology, cellular_automata, long_arithmetic |
| task | Value('string') | Specific task variant (e.g., formal_logic_bottom_up) |
| prompt | Value('string') | Full prompt sent to the model |
| model_response | Value('string') | Complete untruncated model output |
| extracted_answer | Value('string') | Answer extracted by domain-specific parser |
| ground_truth | Value('string') | Expected correct answer |
| correct | Value('bool') | Whether extracted_answer matched ground_truth |
| finish_reason | Value('string') | vLLM finish reason: stop (natural end) or length (hit max_tokens) |
| token_count | Value('int64') | Number of tokens in model_response |
Generation Parameters
{
"script_name": "eval_model.py",
"model": "reasoning-degeneration-dev/algo-sft-formal-logic-truth-table",
"description": "Full eval traces for algo-sft-formal-logic-truth-table across test/harder/ood splits",
"hyperparameters": {
"max_tokens": 32768,
"max_model_len": 32768,
"temperature": 0.0,
"base_model": "Qwen/Qwen2.5-1.5B-Instruct"
},
"input_datasets": []
}
Usage
from datasets import load_dataset
dataset = load_dataset("raca-workspace-v1/algo-sft-eval-traces-formal-logic-truth-table-v4", split="train")
print(f"Loaded {len(dataset)} rows")
Uploaded via RACA hf_utility.
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