Relations and Functions

Relations and Functions

Question

 X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and (X ∩ Y) has 10 elements. How many elements does Y have?

Answer
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  space space space space space space space space straight n left parenthesis straight X intersection straight Y right parenthesis space space equals space 10

            n(X)   =  40
we know that 
space space space space space space space straight n left parenthesis straight X union straight Y right parenthesis space equals space straight n left parenthesis straight x right parenthesis space plus space straight n left parenthesis straight Y right parenthesis space minus space straight n left parenthesis straight X union straight Y right parenthesis

∴         60 = 40 + n(Y) - 10
rightwards double arrow        n(Y) = 60-40+10 = 30
Hence, the number of elements in set Y = 30.

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