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.
