Boolean Simplification questions

Question

I'm having some trouble getting a handle with this course. We are starting Boolean algebra and my professor wants us simplify the following:

Im sorry for the ignorance but I can't find a good reference to solve the problem.

1. $[XY'(Z+YW)+X'Y']Z$
2. $XY'+ X(Y+Z)'+ Y(Y+Z)'$

I am assuming the "()" with "'" means the over-score above the variables.

Answer 1

Use these rules to solve the questions.

1. [XY'(Z+YW)+X'Y']Z => [XY'Z + XY'YW + X'Y']Z (Distributive Law)=> [XY'Z+X'Y']Z (Complementary Law) => XY'Z+X'Y'Z => Y'Z(X+X') (Distributive Law) => Y'Z (Complementary Law followed by Law of Intersection)

2. XY'+ X(Y+Z)'+ Y(Y+Z)'=> XY' + XY'Z' + Y(Y'Z') (De Morgan's Law and Distributive Law)=> XY'(1+Z) (Distributive Law and Complementary Law) => XY' (Law of Union followed by Law of Intersection)