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

Q1. If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X $\cup$ Y ) = 38, find n ( X $\cap$ Y ).

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n( X ) = 17,       n( Y ) = 23             and  n( X $\cup$ Y ) = 38

n( X $\cup$ Y ) = n( X ) + n( Y ) - n ( X $\cap$ Y )

38  =  17 + 23 - n ( X $\cap$Y )

n ( X $\cap$Y ) =  40 - 38

n ( X $\cap$Y ) = 2.

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