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

Question

Philoid · Accepted Answer

Given:

n (A ∪ B) = 50

n(A) = 28

n(B) = 32

To Find:

n (A ∩ B) =?

We know,

n (A ∪ B) = n(A) + n(B) – n (A ∩ B)

Substituting the values we get

50 = 28+32 – n (A ∩ B)

50 = 60 – n (A ∩ B)

–10 = – n (A ∩ B)

∴ n (A ∩ B) = 10.