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?

Answer 1

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.