Q2 of 86 Page 24

If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X ∩ Y have?

Given-


n(X) = 8, n(Y) = 15, and n(X ∪ Y) = 18


We know that-


n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)


⇒ 18 = 8+15 - n(X ∩ Y)


⇒ 18 = 23 - n(X ∩ Y)


⇒ n(X ∩ Y) = 23-18


∴ n(X ∩ Y) = 5


More from this chapter

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7

Fill in the blanks to make each of the following a true statement:

(i) A ∪ A’ = . . . (ii) ϕ’ ∩ A = . . .


(iii) A ∩ A’ = . . . (iv) U’ ∩ A = . . .

 1

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 3

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 4

If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?