#### 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.

Is there an error in this question or solution?

Solution 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? Concept: Practical Problems on Union and Intersection of Two Sets.