If A and B are two sets such than n(A) = 8, n(B) = 11 and n(A ∪ B) = 14 then find n(A ∩ B).

Question

Philoid · Accepted Answer

Given: n(A) = 8, n(B) = 11, n(A ∪ B) = 14

We know that n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

⇒ 14 = 8 + 11 – n(A ∩ B)

⇒ 14 = 19 – n(A ∩ B)

⇒ n(A ∩ B) = 19 – 14

⇒ n(A ∩ B) = 5

Hence n(A ∩ B) = 5