Using propositional logic to show logical equivalence of $\neg (q \to p) \lor (p \land q) \equiv q$

Question

I am trouble to figure out the how to prove the logical equivalence between these two propositions.

I have gotten to where I denote $A := \neg (q \to p) \lor (p \land q)$.

And from $A$ I thought about using the conditional identity where $\neg(\neg q \lor p)$. But after that I'm stuck. If anyone could provide insight that would be great. Thank you!

Answer 1

One may write $$ \begin{align} A &= (¬(q → p)) ∨ (p ∧ q) \\\\&=(¬(¬q ∨ p)) ∨ (p ∧ q) \\\\&=(¬(¬q)∧ (¬p)) ∨ (p ∧ q) \\\\&=(q∧ (¬p)) ∨ (q ∧ p) \\\\&=q∧ (¬p∨ p) \\\\&=q∧ 1 \\\\&=q. \end{align} $$