I\'m having trouble proving the following algebraically (with thebasic axioms an

Question

I'm having trouble proving the following algebraically (with thebasic axioms and theorems):
x'y' + xy = (xy' + x'y)'
Could I get some help on this? Also, I would appreciatethe methodology you used to solve it. I know there's got tobe a simple general methodology for solving these proofs, I justdon't know what it is. Thanks.
x'y' + xy = (xy' + x'y)'
Could I get some help on this? Also, I would appreciatethe methodology you used to solve it. I know there's got tobe a simple general methodology for solving these proofs, I justdon't know what it is. Thanks.

Explanation / Answer

We know that (a+b)' = a'.b'     (xy' + x'y)' = (xy')'. (x'y)'                      = (x'+y) . (x + y')                       = x'x +x'y' + yx +yy'                         = 0 + x'y' +xy+0      [since xx' =0, yy' =0]                          = xy+x'y' Therefore (xy' +x'y)' = xy +x'y'

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