If X and Y are two sets such that X has 40 elements,
Question:

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:

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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