Question

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

(i) n (B)

(ii) n (A – B)

(iii) n (B – A)

Answer 1

(i) n (B)

As we know,

n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

By substituting the values we get

42 = 20 + n (B) – 4

42 = 16 + n (B)

n (B) = 26

∴ n (B) = 26

(ii) n (A – B)

As we know,

n (A – B) = n (A ∪ B) – n (B)

By substituting the values we get

n (A – B) = 42 – 26

= 16

∴ n (A – B) = 16

(iii) n (B – A)

As we know,

n (B – A) = n (B) – n (A ∩ B)

By substituting the values we get

n (B – A) = 26 – 4

= 22

∴ n (B – A) = 22