Simplify(X U Y U Z) n (X U (Y n Z))

Answer 1

Since A∩(BC) = A∩B ∪ A∩C,

your first step is

(X ∪ Y ∪ Z)∩X ∪ (X ∪ Y ∪ Z)∩(Y∩Z)
and now break down each of those similarly. Just review your basic set properties. Recall that X∪X = X∩X = X