If A and B are two sets such that n(A –B) = 24, n(B – A) = 19 and n(A ∩ B) = 11, find:
(i) n(A)
(ii) n(B)
(iii) n(A ∪ B)
Given:
n(A - B) = 24, n(B - A) =19 and n(A ∩ B) = 11
To Find:
(i) n(A)
We know that,
n(A) = n(A - B) + n(A ∩ B)
= 24 + 11
= 35
Therefore, n(A) = 35 …(1)
(ii) n(B)
We know that,
n(B) = n(B - A) + n(A ∩ B)
= 19 + 11
= 30
Therefore,
n(B) = 30 …(2)
(iii) n(A ∪ B)
We know that,
n(A ∪ B) = n(A) + n(B) – n(A ∩ B) {From (1) & (2) n(A) =35
and n(B) =30}
= 35 + 30 - 11
= 54
Therefore,
n(A ∪ B) = 54