TITLE: What's wrong with this truth table for implication?
QUESTION [9 upvotes]: I completed this truth table in an assignment for an implication and got a few of the outputs wrong. I was wondering if anyone can help explain why I got them wrong. This is part of the truth table that I got wrong:
PLEASE FORGIVE THE TYPO IN TABLE 4. It's meant to say $(\neg r \Rightarrow  p) \land (r \Rightarrow q)$ AND NOT $(\neg p \Rightarrow p) \land (r \Rightarrow q)$

REPLY [10 votes]: Seems correct to me
\begin{array}{c:c}p & r & q & \neg r & (¬r \to p) & (r \to q) & (¬r \to p) \wedge (r \to q)
\\ \hdashline 0 & 0 & 0 & 1 & 0 & 1 & 0
\\ \hdashline 0 & 0 & 1 & 1 & 0 & 1 & 0
\\ \hdashline 0 & 1 & 0 & 0 & 1 & 0 & 0
\\ \hdashline 0 & 1 & 1 & 0 & 1 & 1 & 1
\\ \hdashline 1 & 0 & 0 & 1 & 1 & 1 & 1
\\ \hdashline 1 & 0 & 1 & 1 & 1 & 1 & 1
\\ \hdashline 1 & 1 & 0 & 0 & 1 & 0 & 0
\\ \hdashline 1 & 1 & 1 & 0 & 1 & 1 & 1
\end{array}
Edit: Ah.  Trevor has spotted what may have happened.