Question

A and B are two sets such that n(A-B) = 32+x, n(B-A) = 5x and n(AB)= x. Illustrate
the information by means of a Venn diagram. Given that n(A) = n(B), calculate the
value of x.​

Answer 1

Step-by-step explanation:

n(A−B)=32+x

n(B−A)=5x

n(A∩B)=x

n(A)=n(B)

(1)n(A)=n(B)

32+x+x=5x+x

32+2x=6x

6x−2x=32

4x=32

x=8

(2)n(A)=32+x+x

=32+2x

=32+2×8

x=48

n(B)=5x+x

=6x

=6×8

=48

n(A∪B)=n(A)+n(B)−n(A∩B)

=48+48−8

=96−8

=88

so, the value of x=8 and n(A∪B)=88