A and B are two sets such that n(A-B)=20+x, n(B-A)=3x and n(A ∩B)=x+1.Draw a Venn diagram to illustrate this information.Find (i)the value of x (ii)n(AUB)

In this question you have not given that n(A) = n(B).

*Venn diagram:
n(a-b)=20+x*

*n(b-a)=3x*

*n(a* *∩* *b) =x+1*

We know that

*n(a-b) = n(a)-n(a* *∩* *b)*

*∴n(a) = n(a-b) + n(a* *∩* *b)*

*= (20+x) + (x + 1)*

*= 2x + 21*

Similarly,* n(b) = n(b-a) + n(a* *∩* *b)*

*=3x + (x+1)*

*=4x + 1*

According to the question,

*n(a) = n(b)*

*∴2x + 21 = 4x +1*

*⇒2x = 20*

*∴* *x = 10*

**
**