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If X and Y are two sets, such that X ∪ Y has 40 elements, X has 28 elements and Y has 22 elements, how many elements does X ∩ Y have ?

If X and Y are two sets, such that X ∪ Y has 40 elements, X has 28 elements and Y has 22 elements, how many elements does X ∩ Y have ? Correct Answer 10

Concept:

n(A ⋃ B) = n(A) + n(B) – n(A ⋂ B)

 

Calculation:

Here, n(X ∪ Y) = 40 , n(X) = 28, n(Y) = 22

n(X ⋃ Y) = n(X) + n(Y) – n(X ⋂ Y)

⇒ n(X ∩ Y) =  - n(X ⋃ Y) 

= (28 + 22) - 40

= 10

Hence, option (3) is correct.

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