Switching Algebra proof question

[ilikescience]

Homework Statement

Prove with algebraic manipulation the following equality: X Y' + Y Z' + X' Z = X' Y + Y' Z + X Z'

Homework Equations

All you need to know to prove it are the switching axioms and theorems listed on the second slide of http://meseec.ce.rit.edu/eecc341-winter2001/341-12-13-2001.pdf" .

The Attempt at a Solution

xy' + yz' + x'z = (xy' + yz' + x'z)' ' involution
= ((x'+y)(y'+z)(x+z'))' DeMorgan
= (xyz + x'y'z')' distribute and use aa' = 0
= (x' + y' + z')(x + y + z) DeMorgan
= (xy' + yz' + x'z) + (x'y + y'z + xz') distribute and use aa' = 0

since we have a = a + b then b = a or b = 0 by idempotency or identities, but I think we can show b ~= 0 if x, y ,or z are not all 0 or 1.

I feel like there might be an easier way. What do you think?

 

[Zayer]

all you need are distribution ,aa=a and a+a'=1

there is no need for DeMorgan or anything else