Question

If A and B are two sets such that n(A) = 100, n(B) = 150 and n(A  B) = 50. Find the following values : (i) n(A U B) (2) (ii) n(A – B)​

Answer 1

Given : A and B are two sets such that n(A) = 100, n(B) = 150 and n(A ∩ B) = 50.

To Find : the following values : (i) n(A U  B) (ii) n(A – B)​

Solution:

n(A U  B)  = n(A) + n(B) - n(A ∩ B)

=>  n(A U  B)  = 100 + 50  - 50

=> n(A U  B)  =  100

n(A U  B)  =  100  n(A) = 100

A ⊂ A U  B

Hence A = A U  B

=> B ⊂ A

B ⊂ A Hence

n(A – B)​  = n(A) - n(B)

=> n(A – B)​  = 100 - 50

=> n(A – B)​  = 50

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