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Intersection

If n A =12,...

Question

If $n (A) = 12, n (B) = 17$ and $n (A \cup B) = 21$ , find $n (A \cap B)$

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Solution

$n (A) = 12$
$n (B) = 17$
$n (A \cup B) = 21$
$n (A \cap B) = n (A) + n (B) - n (A \cup B)$
$= 12 + 17 - 21$
$= 29 - 21 = 8$
$n (A \cap B) = 8$

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