NCERT Class XI Mathematics - Sets - Solutions
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Question : 51
Total: 73
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?
Solution:
Here n(X ∪ Y) = 18, n(X) = 8 and n(Y) = 15
We know that
n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)
⇒ 18 = 8 + 15 – n(X ∩ Y) ∴ n(X ∩ Y) = 23 – 18 = 5.
We know that
n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)
⇒ 18 = 8 + 15 – n(X ∩ Y) ∴ n(X ∩ Y) = 23 – 18 = 5.
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