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If X and Y are two sets such that X ∪ Y has 70 elements, X has 38 elements and Y has 42 elements, how many elements does X ∩ Y have? 

If X and Y are two sets such that X ∪ Y has 70 elements, X has 38 elements and Y has 42 elements, how many elements does X ∩ Y have?  Correct Answer 10

Concept:

n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)

Calculation:

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Given: n (X ∪ Y) = 70, n (X) = 38, n (Y) = 42

By using the formula,

n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)

⇒ n(X ∩ Y) = n (X) + n (Y) – n (X ∪ Y)

⇒ n(X ∪ Y) = 38 + 42 – 70

∴ n(X ∪ Y) = 10

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