# Can (x'y' + xy) be simplified?

I started with (AB' + A'B)' and ended up with (A'B' + AB). Is this all the farther I can go? I feel like this is always going to be true, but I'm not sure how to prove it algebraically.

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$(fg)'=fg'+f'g, (fg)''=f''+2f'g+2fg'+g''$ etc. what are $x$ and $y$? what are you asking? –  yoyo Apr 13 '11 at 1:25
sorry, should have used A and B instead of x and y...A and B are booleans. –  Marty Apr 13 '11 at 1:33
What do you mean by simpler? Fewer gates (AND/NOT/OR)? Smaller length when viewed as a string? –  Aryabhata Apr 13 '11 at 1:37
In a sense, this is the farthest you can go. What you have reached is the equivalence operation, which is the negation of XOR. –  Brandon Carter Apr 13 '11 at 2:31
@Brandon: You should probably write that as an answer. –  Ben Alpert Apr 13 '11 at 4:29

"Nex or"? :) –  bcat Apr 26 '11 at 4:54