Need help with Infinite sets

Question

If A and B are infinite sets, A∩B must be an infinite set. Is this true? Please explain.

Answer 1

This statement is false.  Example:  Set A could be the set of all non-negative integers (i.e. {0,1,2,3,4.......}).  Set B could be the set of all non-positive integers (i.e. {0, -1, -2, ......}).  Set A and B are both infinite sets but A∩B is simply {0} as they only have zero in common.