Q5 of 86 Page 24

If 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?

Given-


n(X) = 40, n(X ∩ Y) = 10, and n(X ∪ Y) = 60


We know that-


n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)


⇒ 60 = 40+n(Y) - 10


⇒ 60 = 30+n(Y)


⇒ n(Y) = 60-30


∴ n(Y) = 30


Thus, the no. of elements in n(Y) is 30.


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