If X and Y are two sets such that X has 40 elementsX Yhas 60 elements andX Yhas 10 elements, how many elements does Y have?

Here n(X) = 40,n(X Y) = 60andn(X Y) = 10 We know thatn(X Y) = n(X) + n(Y) - n(X Y) 60 = 40 + n(Y) - 10 n(Y) = 60 - 30 = 30.

If X and Y are two sets such that X has 40 elementsX Yhas 60 elem…

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Question

If X and Y are two sets such that X has 40 elements$X \cup Y$has 60 elements and$X \cap Y$has 10 elements, how many elements does Y have?

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Answer

Here n(X) = 40,$n(X \cup Y) = 60$and$n(X \cap Y) = 10$
We know that$n(X \cup Y) = n(X) + n(Y) - n(X \cap Y)$
60 = 40 + n(Y) - 10
$\therefore n(Y) = 60 - 30 = 30.$

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