Decide whether the following propositions are true or false, providing a short justification for each conclusion.

(a) If every proper subsequence of (xn) converges, then (xn) converges as well.
(b) If (xn) contains a divergent subsequence, then (xn) diverges.
(c) If (xn) is bounded and diverges, then there exist two subsequences of (xn) that converge to different limits.
(d) If (xn) is mo