Question

Let A and B be two sets such that n(A)=20, n(AUB)=42, n(AintersectionB)=4.

Find i) n(B)

ii) n(A-B)

iii) n(B-A)

Answer 1

Given:
n(A)=20,

n(A∪B)=42

n(A∩B)=4

(i)

n(A∪B)=n(A)+n(B)−n(A∩B)

42=20+n(B)−4

n(B)=42−20+4=26


(ii

n(A−B)=n(A)−n(A∩B)

n(A−B)=20−4=16


(iii

n(B−A)=n(B)−n(A∩B)

n(B−A)=26−4=22

hope it helps mate