Question 5:
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?
Answer
It is given that:
n(X) = 40, n(X ∪ Y) = 60, 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 − (40 − 10) = 30
Thus, the set Y has 30 elements.
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