Relations and Functions

Relations and Functions

Question

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

Answer

n(X)  =  17
n(Y) =  23
space space space space space space space straight n left parenthesis straight X space union space straight Y right parenthesis space space equals space 38
We know that
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∴   space space space space space space space space space space space space 38 space equals space 17 space plus 23 space minus space straight n left parenthesis straight X intersection straight Y right parenthesis

rightwards double arrow    space space space space straight n left parenthesis straight X intersection straight Y right parenthesis space = 17 + 23 -38 = 2

Hence,  space space space space space space space space straight n left parenthesis straight X space intersection space straight Y right parenthesis space equals space 2

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