If X and Y are two sets and X′ denotes the complement of X, then X∩(X∪Y)′ is equal to
X
Y
ϕ
X∩Y
X∩(X∪Y)′=X∩(X′∩Y′) [∵(A∪B)′=A′∩B′]=(X∩X′)∩Y′=ϕ∩Y′=ϕ [∵ϕ∩A=ϕ]