Q1 of 86 Page 24

If X and Y are two sets such that n (X) = 17, n (Y) = 23 and n ( X ∪ Y ) = 38, find n ( X ∩ Y ).

Given-


n(X) = 17, n(Y) = 23, and n(X ∪ Y) = 38


We know that-


n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)


⇒ 38 = 17+23 - n(X ∩ Y)


⇒ 38 = 40 - n(X ∩ Y)


⇒ n(X ∩ Y) = 40-38


∴ n(X ∩ Y) = 2


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