If A and B are two sets such that n(A) = 37, n(B) = 26 and n (A ∪ B) = 51, find n (A ∩ B).

Question

Philoid · Accepted Answer

Given:

n(A) = 37

n(B) = 26

n(A ∪ B) = 51

To Find: n(A ∩ B)

We know that,

|A ∪ B| = |A| + |B| - |A ∩ B| (where A and B are two finite sets)

Therefore,

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

51 = 37 + 26 – n(A ∩ B)

n(A ∩ B) = 63 – 51 = 12

Therefore,

n(A ∩ B) = 12