Given the following two propositional forms, prove whether or not they are logically equivalent.
$(a \wedge \neg c) \vee (b \wedge c)$
$(a \wedge \neg c) \vee (b \wedge c) \vee (a \wedge b)$
I've written out a truth table for both expressions, and I can see that they are in fact logically equivalent; however, I was wondering how to go about approaching this problem more elegantly using rules of equivalence as opposed to a brute force truth table solution. Thank you!