Question

Let A and B be two sets such that n( A) = 20, n(A ∪ B) = 42, n(A ∩ B) = 4. Find

1. n(B)

2. n(B – A) 

3. n(A – B)

Answer 1

1. n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

⇒ 42 = 20 + n(B) – 4 ⇒ n(B) = 26

2. n(B – A) = n(B) – n(A ∩ B) = 26 – 4 = 22

3. n(A – B) = n(A) – n(A ∩ B) = 20 – 4 = 16.