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

30 Elements

Given:

n(X) = 40

n(X U Y) = 60

n(X ⋂ Y) = 10

To Find:

n(Y) = ?

Calculating:

The Formula used to find the union of sets is:

n(X U Y) = n(X) + n(Y) - n(X ⋂ Y)

Taking n(X) and - n(X ⋂ Y) to the other side of the formula we get:

n(Y) = n(X U Y) - n(X) + n(X ⋂ Y)

Substituting all the values that are known to us in this formula we get:

n(Y) = 60 - 40 + 10

n(Y) = 20 + 10

n(Y) = 30

Therefore, Element Y has 30 Elements.