How to prove this using laws?

Question

How do they prove this?

$$(p\to q)\land[\neg q\land(r\lor\neg q)]\equiv\neg q\land\neg p$$

Answer 1

HINT: One of the absorption laws tells you that $\neg q\land(r\lor\neg q)\equiv\neg q$, so the lefthand side is equivalent to

$$(p\to q)\land\neg q\;.$$

Now use the fact that $p\to q$ is equivalent to $\neg p\lor q$, apply a distributive law, and do a little simplifying.