# Booleans: Solve Algebraically

Prove using Prove algebraically : 1) x'′⊕ y = x⊕y' = (x⊕y)'

2) x⊕1 = x'

3) x⊕x' = 1

4) (A+B)(A'C'+C)(B'+AC') = A'B $(A+B)(A'.C'+C)(B'+AC)' = A'B$

I know x⊕y = xy'+x'y But how do i deal with X'⊕Y? What does that become?

And for 4) I did:

(A+B)[(X+Y)'+C] [B.(AC)']

(A+B)[(A+B)'+C] [(B.(A'+B')]

then what do I do from here?

And this question just makes my balls sweat omg.. http://i.imgur.com/CPlRB91.png

Been having trouble solving these questions of my homework. Thank You!

-
What is the distinction between proving "algebraically" and "using Booleans"? –  Chris Eagle Feb 2 '13 at 10:27
none, its just the way the question was formatted :P –  lunapt Feb 2 '13 at 10:55
It might be extremely helpful if you provide some background to what you're doing. I do know a bit about boolean algebras, but I'm afraid I can't make head nor tail out of your question. Usually they come with two binary operations, but you seem to be having four. And in the situation I know, the 4th statement doesn't seem to be true - even if I interpret the lower dot as one that can be omitted. (where exactly should the prime be? within the brackets or outside? - notice that at least usually $A'C'=AC$) –  HSN Feb 2 '13 at 10:59
circuit design math –  lunapt Feb 2 '13 at 22:52