[Step-by-Step] For each of the following statements determine whether the statement is true or false. If the statement is false give a counterexample. If


Question: For each of the following statements determine whether the statement is true or false. If the statement is false give a counterexample. If the statement is true, provide a brief justification.

  1. A subsequence of a bounded sequence is bounded
  2. A subsequence of a monotone sequence is monotone.
  3. A subsequence of a convergent sequence is convergent.
  4. A sequence converges if it has a convergent subsequence.

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