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?

Asked by Sudhanshu | 11 months ago |  98

1 Answer

Solution :-

Given

n (X U Y) = 18

n (X) = 8

n (Y) = 15

We can write it as

n (X U Y) = n (X) + n (Y) – n (X ∩ Y)

Substituting the values

18 = 8 + 15 – n (X ∩ Y)

By further calculation

n (X ∩ Y) = 23 – 18 = 5

So we get

n (X ∩ Y) = 5

Answered by Sudhanshu | 11 months ago

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