Question

Sitha said that, "If A and B are disjoint sets then n(AUB) = n(A) + n(B)". Is she correct? Justify your
answer.​

Answer 1

The statement Sitha said "If A and B are disjoint sets then n(A∪B) = n(A) + n(B)" is correct.

• Disjoint sets are the sets whose intersection is zero, i.e, they don't have any elements in common.

             ⇒  A∩B = ∅

             ⇒  n(A∩B) = 0  ----------------(1)

• We know that

                n(A∪B) = n(A) + n(B) - n(A∩B)

          ⇒   n(A∪B) = n(A) + n(B) - 0         [∵ From (1)]

          ⇒   n(A∪B) = n(A) + n(B)