use the law of algebra of sets to that $\displaystyle

((X \cup Y) \cap (X \cup Y')) \cap ((X' \cup Y) \cap (X' \cup Y')) \;=\;\emptyset

$ please specify which rules you use in the derivation....

the laws i've been given for set operations are.....

idempotent laws

associative laws

commutative laws

distributive laws

identity laws

Involution laws

involution laws

complement laws

de morgans laws