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