1. Let a, b, c, d be real numbers where a

1. Let a, b, c, d be real numbers where a < b and c < d. (a) Give a very good proof that shows (a, b) and (c, d) have the same cardinality (i.e "are equivalent" ). (b) Give a very good proof that shows the set R (i.e. the set of real numbers) and the open interval (a, b) have the same cardinality.