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

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If A and B are two sets and U is the universal set such that n(U)=700,n(A)=200,n(B)=300 and n(A∩B)=100, find n(A′∩B′).

We need to find n(A′∩B′)n(A′∩B′)=n(U)−n(A∪B) ....(i)Now n(A∪B)=n(A)+n(B)−n(A∩B)n(A∪B)=400Put in equation (i), we getn(A′∩B′)=700−400=300

If $A$ and $B$ are two sets and $U$ is the universal set such that $n (U) = 700, n (A) = 200, n (B) = 300$ and $n (A \cap B) = 100$ , find $n (A^{'} \cap B^{'})$ .

We need to find $n (A^{'} \cap B^{'})$
$n (A^{'} \cap B^{'}) = n (U) - n (A \cup B)$ ....(i)
Now $n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$n (A \cup B) = 400$
Put in equation (i), we get
$n (A^{'} \cap B^{'})$ $= 700 - 400 = 300$