Question 2:
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?
Answer
It is given that:
n(X ∩ Y) = ?
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
∴ n(X ∩ Y) = 5
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