Question

THINK & DISCUSS
1. What is the relation between n(A), n(B) n(
AB) and n(AUB)
2. If Aand B are disjoint sets, then how can you find n(AUB)​

Answer 1

Relation:

n(A∪B) = n(A) + n(B) - n(A∩B)

Note that A-B, A∩B and B-A are disjoint and their union is AUB Therefore.

n(AUB) = n(A-B) + n(A∩B) + n(B-A)

on adding and subtracting n(A∩B) we get

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

Therfore:

n(A∪B) = n(A) + n(B) - n(A∩B)