Simplify Boolean algebra

Question

f(X,Y,Z)=(X’Y+XZ)(X+Y’)

Answer 1

Use the distributive properties:

(X’Y+XZ)(X+Y’)
=X(X’Y+XZ) + Y’(X’Y+XZ)
=(XX'Y + XXZ) + (X'YY' + XY'Z)
=(Y+XZ) + (X'+XY'Z) [XX'=YY'true, XX=X]
=Y + X' + XZ + XZY'
=Y + X' + XZ [XZ+XZY' = XZ (absorption)]

Now your turn to do some work:
check the above simplification using a truth table on the original expression, and the simplified version.