Exercise 2.5.2. Decide whether the following propositions are true or false, roviding a short justification for each conclusion. (a) If every proper subsequence of (n) converges, then (n) converges as well. (b) If (rn) contains a divergent subsequence, then (n) diverges. (c) If (n) is bounded and diverges, then there exist two subsequences of (rn) that converge to different limits.

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