If n(∪)=700, n(A)=200, n(B)=300 and n(A∩B)=100, the

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If n (\cup) = 700, n (A) = 200, n (B) = 300

and

n (A \cap B) = 100,

then

n (A^{^{'}} \cap B^{^{'}}) =

___.

Options:

A . 400

B . 240

C . 300

D . 500

Answer: Option C
:
C
From de-Morgan's law of complementation, we have

A^{'} \cap B^{'} = (A \cup B)^{'} .

\Rightarrow n (A^{'} \cap B^{'}) = n ((A \cup B)^{'})

But,

n ((A \cup B)^{'}) = n (U) - n (A \cup B)

by definition of complement of a set.

∴ n (A^{'} \cap B^{'}) = n (U) - n (A \cup B)

= n (U) - [n (A) + n (B) - n (A \cap B)]

= 700 - (200 + 300 - 100)

= 300

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