TITLE: Proving $(p \land \lnot q) \rightarrow p$ is a tautology using logical equivalences
QUESTION [5 upvotes]: I'm very new to discrete math and propositional calculus. 
I keep getting lost trying to prove the following propositional formula is a tautology using equivalencies. 
$$(p \land \lnot q) \rightarrow p$$
Edit: I solved it; see my answer below.

REPLY [7 votes]: Figured it out with amWhy's help. 
$(p \land \lnot q) \rightarrow p \equiv \lnot (p \land \lnot  q) \lor p $, 
As such, $\lnot (p \land \lnot q) \lor p$
Then, we use DeMorgan's law to get $(\lnot p \lor q) \lor p$, 
Then, using association, $q \lor (\lnot p \lor p) $, 
$q \lor T $, 
T
Therefore, $(p \land \lnot q) \rightarrow p$ is a Tautology.