The question presented was to use boolean algebra to show that
XY’Z + X’Y’Z’ + XY’Z’ + X’YZ’ ≡ XYZ’ + XY’Z + XY’Z’ + XYZ’
I've tried using various laws of Boolean algebra, but the answer that I always end up with is
X' ≡ XY or X ≡ X' + Y'
Obviously neither are true. I tried plugging these functions into a truth table to verify the equivalence that way, but the outputs were different for both functions.
Is there an error in the question or am I missing something?
Here is the work I've done to reach my solution:
XY'Z + XY'Z' + X'YZ'+ X'Y'Z' == XYZ' + XYZ' + XY'Z + XY'Z'
X'YZ'+ X'Y'Z' == XYZ' by removing like terms
Z'(X'Y + X'Y') == Z'(XY) using distributive and associative law
X'Y + X'Y' = XY by removing like terms
X'Y + X'Y' = X' + Y' DeMorgan's
(X + Y')(X + Y) = X' + Y' DeMorgan's
X(Y + Y') = X' + Y' Distributive Law
X = X' + Y' by Inverse Law
X' = XY DeMorgan's
False, not equivalent.