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Given n(A) = 7; n(B) = 8 and n(A ∪ B) = 10 find n[P(A ∩ B)].

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Given n(A) = 7; n(B) = 8 and n(A ∪ B) = 10 find n[P(A ∩ B)].

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n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

(i.e.,) 10 = 7 + 8 – n(A ∩ B) 

⇒ n(A ∩ B) = 7 + 8 – 10 = 5 

So n[P(A ∩ B)] = 25 = 32

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