TITLE: Simplify $p\lor q\lor(\neg p\land\neg q\land r)$ to $p\lor q\lor r$
QUESTION [0 upvotes]: 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!

REPLY [3 votes]: $$p\lor q\lor(\neg p\land\neg q\land r)$$
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:
$$=p\lor q\lor r$$
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