Simplify $(x'+y)'(x+y)'$ with boolean algebra

Question

So I'm doing some homework and trying to simplify $(x'+y)'(x+y)'$. So far these are the steps I've completed, but I'm not 100% sure that they're appropriate.

$(x'+y)'(x+y)' = (x'+y)'(x’y’)$

$(x'+y)'(x’y’) = (x’’+ y’)(x’y’)$

$(x’’+y’)(x’y’) = (x+y’)(x’y’)$

I'm unsure of what to do after this step (or if I've made any actual mistakes)

use DeMorgan's theorem twice on each term in the product first. Then multiply out and you will have your answer. Truth Tables are not required here. — F.N., Sep 25 '21 at 07:14

score 0 · Answer 1 · answered Oct 29 '14 at 02:32

0

$(x'+y)'(x+y)'=(x'+y)'(x'y')=(x''y')(x'y')=(xy')(x'y')$

Can you do the last step?

answered Oct 29 '14 at 02:32

JRN

6,566

I couldn't figure it out algebraically so I drew out a truth table to figure it out and realized it was 0. – secondubly Oct 29 '14 at 03:04

Simplify $(x'+y)'(x+y)'$ with boolean algebra

1 Answers1