Let (M. d) be a metric space and let {an} and {bn} be two sequences in M such that lim(ninifinity) d(an, bn) = 0. Prove the following statements. (a) The sequence {an} is convergent if and only if the sequence {bn} is convergent. (b) The sequence {an) is a Cauchy sequence if and only if {bn} is a Cauchy sequence.