1. The problem statement, all variables and given/known data Prove with algebraic manipulation the following equality: X Y' + Y Z' + X' Z = X' Y + Y' Z + X Z' 2. Relevant 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" [Broken]. 3. 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?