NIMCET 2011 Question Paper with solutions

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Question : 22 of 120

Marks: +1, -0

Let

X

be the universal set for sets

A

and

B

. If

n(A)=200, n(B)=300

and

n(A ∩ B)=100

, then

n(A^{'} ∩ B^{'})

is equal to 300 provided

n(X)

is equal to

600
700
800
900

Solution:

Now,

n(A ∪ B)=n(A)+n(B)-n(A ∩ B)

=200+300-100=400

Also,

n(A^{'} ∩ B^{'})=300

⇒ n(A ∪ B)^{'}=300

⇒ n(X)-n(A ∪ B)=300

⇒ n(X)=300+400=700

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