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Question

If $A$ and $B$ are two sets such that $n (A \cup B) = 50$ , $n (A) = 25$ and $n (B) = 32$ then find $n (A \cap B)$

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Solution

$n (A \cup B) = 50$
$n (A) = 25$
$n (B) = 32$
$n (A \cap B) = n (A) + n (B) - n (A \cup B)$
$= 25 + 32 - 50$
$= 57 - 50$
$= 7$
$n (A \cap B) = 7$

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