Question

A and B are two sets such that n( A − B) = 20 + x and n( B – A) = 3x. If n(A) = n(B) then what is the value of x?

Answer 1

Step-by-step explanation:

We know that

n(A) = n(A - B) + n(A∩B)

n(A) = 14 +x + x

n(B) = n(B - A) + n(A∩B)

n(B) = 3x + x

Given n(A) = n(B)

⇒ n(A - B) + n(A∩B) = n(B-A) + n(A∩B)

⇒14+2x = 3x + x

⇒14 = 2x

∴ x = 7.