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Intersection

If nA=30, ...

Question

If $n (A) = 30$ , $n (B) = 40$ and $n (A \cup B) = 52$ then find $n (A \cap B)$

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Solution

$n (A \cup B) = n (A) + n (B) - n (A \cap B) 52 = 30 + 40 - n (A \cap B) n (A \cap B) = 70 - 52 n (A \cap B) = 18$

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