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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? - Mathematics

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Question

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?

Solution

It is given that:

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

We know that:

n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)

∴ 60 = 40 + n(Y) – 10

∴ n(Y) = 60 – (40 – 10) = 30

Thus, the set Y has 30 elements.

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Solution 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? Concept: Practical Problems on Union and Intersection of Two Sets.
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