Discrete: Boolean Function

Question

~(pV~q) v (~p^~q) is equal to ~p?

I know the answer is yes and I've been using DeMorgans initially then distributive law after. However I keep messing up on the algebra. Help is appreciated so I can catch where I'm going wrong.

methods to check your calculation are explained here – miracle173 Sep 29 '13 at 21:49 — miracle173, Sep 29 '13 at 21:49

score 1 · Answer 1 · answered Sep 29 '13 at 21:57

1

$$\begin{align} \lnot (p \lor \lnot q) \lor (\lnot p \land \lnot q & \equiv (\lnot p \land q) \lor (\lnot p \land \lnot q) \tag{DeMorgan's} \\ \\ &\equiv \lnot p \land \underbrace{(q\lor \lnot q)}_\text{true}\tag{Distributive Law} \\ \\ &\equiv \lnot p\end{align}$$

answered Sep 29 '13 at 21:57

amWhy

209,954

Thanks, @Amzoti, for all the support! – amWhy Sep 30 '13 at 01:04

score 0 · Accepted Answer · answered Sep 29 '13 at 21:47

0

$$\neg(p\vee\neg q)\vee(\neg p\wedge\neg q)\equiv(\neg p\wedge q)\vee(\neg p\wedge\neg q)\equiv\neg p\wedge(q\vee\neg q)$$

answered Sep 29 '13 at 21:47

Cameron Buie

102,994

Discrete: Boolean Function

2 Answers2