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 - Maths - Sets

Question

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)

Himanshu · Accepted Answer

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 $n (A \cup B) = n (A - B) + n (A \cap B) + n (B - A) = 20 + x + x + 1 + 3 x = 21 + 4 x = 61$

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)