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Definition of Sets

If n A∩ B =...

Question

If $n (A \cap B) = 5, n (A \cup B) = 35, n (A) = 13,$ find $n (B)$ .

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Solution

$n (A \cap B) = 5$
$n (A \cup B) = 35$
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$35 = 13 + n (B) - 5$
$35 = 8 + n (B)$
$n (B) = 35 - 8$
$n (B) = 27$

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