Let X be the universal set for sets A and B- If nA-200-nB-300 and nA- B-100- then nA- B- is equal to 300 provided nX is equal to

Let U be the universal set containing 700 elements. If A, B are sub-sets of U such that n (A) = 200, n(B) =300 and $n (A \cap B)$ = 100. Then , $n (A^{'} \cap B^{'}) =$

Q. Let

n (U) = 700, n (A) = 200, n (B) = 300

and

n (A \cap B) = 100

, then

n (A^{c} \cap B^{c})

equals to

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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

The correct option is C 700We know thWe know thatn(A∪B)=n(A)+n(B)−n(A∩B)∴n(A∪B)=200+300−100=400Also, n(A′∩B′)=n(X)−n(A∪B)∴300=n(X)−400⇒n(X)=700

Let $X$ be the universal set for sets $A$ and $B$ . If $n (A) = 200, n (B) = 300$ and $n (A \cap B) = 100$ , then $n (A^{'} \cap B^{'})$ is equal to $300$ provided $n (X)$ is equal to

The correct option is C $700$
We know thWe know that
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$∴ n (A \cup B) = 200 + 300 - 100 = 400$

Also, $n (A^{'} \cap B^{'}) = n (X) - n (A \cup B)$
$∴ 300 = n (X) - 400 \Rightarrow n (X) = 700$