Simplify $p\lor q\lor(\neg p\land\neg q\land r)$ to $p\lor q\lor r$

Question

I am trying to simplify the logic expression: $$p\lor q\lor(\neg p\land\neg q\land r)$$ with laws of logic to get: $$p\lor q\lor r$$ I have no idea how to get to the result by using the laws of logic. Help!

Answer 1

$$p\lor q\lor(\neg p\land\neg q\land r)$$ Use the distributive law: $$=(p\lor q\lor\neg p)\land(p\lor q\lor\neg q)\land(p\lor q\lor r)$$ Complementarity ($p\lor\neg p=1$) reduces the first two terms to 1: $$=1\land1\land(p\lor q\lor r)$$ Identity ($p\land1=p$) eliminates those 1s: $$=p\lor q\lor r$$