Question

Suppose n(X) = 28 and n(Y) = 19.

a) What is the maximum number of elements X ∪ Y can have?
B) What is the minimum number of elements X ∪ Y can have?

Answer 1

`n(X\cup Y)=n(X)+n(Y)-n(X\cap Y)`

If
`X` and
`Y` share no common elements, then
`n(X\cap Y)=0`, which means
`n(X\cup Y)=n(X)+n(Y)=47`

On the other hand, if the smaller set is entirely contained within the larger set, i.e.
`Y\subseteq X`, then
`X\cap Y=Y`, and so
`n(X\cup Y)=n(X)+n(Y)-n(Y)=n(X)=28`.