Simplify this boolean expression

Question

$$ \neg P\lor(P \land Q) $$

I want the above expression to be equivalent to

$$\neg P \lor Q$$

But I don't understand how to prove this. Any ideas? Thanks.

Answer 1

Using the distributive law,

¬P∨(P∧Q) = (¬P∨P)∧(¬P∨Q)

But ¬P∨P is always true, so the above

= ¬P∨Q