Question

if n(A) = 20,n(B) =30 and n(A/B) = 10,then find n(AUB).

Answer 1

Answer: 10

Step-by-step explanation:We know that for any two finite sets A and B, n(A∪B)=n(A)+n(B)−n(A∩B).

Here, it is given that n(A)=20,n(B)=30 and n(A∪B)=40, therefore,

n(A∪B)=n(A)+n(B)−n(A∩B)

⇒40=20+30−n(A∩B)

⇒40=50−n(A∩B)

⇒n(A∩B)=50−40

⇒n(A∩B)=10

Hence, n(A∩B)=10