Let A and B be sets. Prove that
(a) If A is a finite set, then A∩B is a finite set.
(b) If A∪B is a finite set, then A and B are finite sets.
(c) If A∩B is an infinite set, then A is an infinite set.
(d) If A is an infinite set or B is an infinite set, then A∪B is an infinite set.