# Simplify this Boolean expression?

X Y Z+X Y' Z'+X' Y' Z+X' Y Z'

I know it simplify to (X XOR Y XOR Z),BUT I want to simplified using only AND, OR, and NOT Gates?

• If you want a sum of products, then $X Y Z+X Y' Z'+X' Y' Z+X' Y Z'$ is as simplified as you can get it. – Adriano Oct 4 '14 at 0:08
I suppose the prime means negation and then $X'=1+X$ etc.
$XYZ+XY'Z'+X'Y'Z+X'YZ'=$ $XYZ+X(1+Y)(1+Z)+(1+X)(1+Y)Z+(1+X)Y(1+Z)=$ $XYZ+X(1+Y+Z+YZ)+(1+X+Y+XY)Z+(Y+XY)(1+Z)=$ $XYZ+X+XY+XZ+XYZ+Z+XZ+YZ+XYZ+Y+YZ+XY+XYZ=$ $X+Y+Z$
Since $X+Y=(X\vee Y)\wedge \neg(X\wedge Y)$ just use AND, OR and NOT to construct $X+Y+Z$, that is $X$ XOR ($Y$ XOR $Z$)