NCERT Class XI Mathematics - Sets - Solutions
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Question : 54
Total: 73
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:
Here n(X) = 40, n(X ∪ Y) = 60 and 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 – 30 = 30.
We know that
n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)
⇒ 60 = 40 + n(Y) – 10 ∴ n(Y) = 60 – 30 = 30.
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