Question

If n(A-B) = 10, n(B-A) = 8 and n(A∩B) = 3, find n(A∪B)​

Answer 1

Answer:

From the question it is given that,

n(A−B)=12

n(B−A)=16

n(A∩B)=5

(i) n(A)

We know that, n(A)=n(A−B)+n(A∩B)

=12+5

=17

(ii) n(B)

We know that, n(B)=n(B−A)+n(A∩B)

n(B)

=16+5

=21

(iii) n(A∪B)

We know that, n(A∪B)=n(A)+n(B)−n(A∩B)

=17+21−5

=38−5

n(A∪B)=33

Answer 2

From the question it is given that,

n(A−B)=12

n(B−A)=16

n(A∩B)=5

(i) n(A)

We know that, n(A)=n(A−B)+n(A∩B)

=12+5

=17

(ii) n(B)

We know that, n(B)=n(B−A)+n(A∩B)

n(B)=16+5

=21

(iii) n(A∪B)

We know that, n(A∪B)=n(A)+n(B)−n(A∩B)

=17+21−5

=38−5

n(A∪B)=33