Question

Suppose X and Y are non-empty sets. Which set contains more elements: X U Y or X ∩ Y? Explain.

Answer 1

Answer:

The union of two sets is guaranteed to result in an equal or larger set than if they were intersected.

This only makes sense because intersecting sets is exceptional, only values that already exist in both sets are in the result.  Whereas a union of two sets gives you all of the content of both.

The only time when an intersection is even equal to a union is when the two sets are identical.  If they aren't then the intersection will be smaller.