Question

We form the intersection of two sets. We know that one of them has n elements and the other has m elements. What can we infer about the cardinality of their intersection?

Answer 1

Cardinality of a finite set is the number of element in it. If one set has n elements, and the other has m elements, then their intersection can contain at most the number of elements which is minimum among n and m. Thus, the cardinality of intersection is less than or equal to $\min(n, m)$.

Answer. Less than or equal to $\min(n, m)$.