Let x ϵ A and y ϵ B

A – B = The set of values of A that are not in B.

A ∩ B = The set containing common values of A and B

B – A = The set of values of B that are not in A.

Two sets X and Y are called disjoint if,

X ∩ Y = ϕ

(A – B) ∩ (A ∩ B) = ((A – B) ∩ A) ∪ ((A – B) ∩B)

(A – B) ∩ (A ∩ B) = ϕ ∪ ϕ

(A – B) ∩ (A ∩ B) = ϕ

Similarly,

(B – A) ∩ (A ∩ B) = ((B – A) ∩ A) ∪ ((B – A) ∩B)

(B – A) ∩ (A ∩ B) = ϕ

Hence, the three sets are pair wise disjoint.