For a sequence {xn} in a metric space X, prove each of thefollowing by generalizing the corresponding proofs for R.
(a) A point x is a cluster point of {xn} iff there is asubsequence of {xn} which converges to x.
(b) If {xn} is convergent with limit x, then x is the uniquecluster point of {xn}.
(c) If {xn} is convergent then {xn} is Cauchy.
(d) If {xn} is Cauchy and x is a cluster point of {xn}, then{xn} converges to x.
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