Question

If A and B are two sets such that n (A ∪ B) = 50, n (A) = 28 and n (B) = 32, find n (A ∩ B).

Answer 1

Here, we have,

n (A ∪ B) = 50

n (A) = 28

n (B) = 32

As we know that, n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

On substituting the values we get

50 = 28 + 32 – n (A ∩ B)

50 = 60 – n (A ∩ B)

–10 = – n (A ∩ B)

∴ n (A ∩ B) = 10