8. Definition: A set A is finite if there exists a non-negativeinteger c such that there exists a bijection from A to {n ? N : n ?c}. (The integer c is called the cardinality of A.)
(a) Let A be a finite set, and let B be a subset of A. Provethat B is finite. (Hint: induction on |A|. Note that our proofcan’t use induction on |B|, or indeed refer to “the number ofelements in B” at all, because we don’t yet know that B isfinite!)
(b) Prove that the union of two disjoint finite sets isfinite.
(c) Prove that the union of any two finite sets is finite.(Hint: A ? B = A ? (B ? A))
