For each of the following, prove or give a counterexample.
(a) If (sn) and (tn) are divergent sequences, then (sn + tn) diverges.
(b) If (sn) and (tn) are divergent sequences, then (sntn) diverges.
(c) If (sn) and (sn + tn) are convergent sequences, then (tn) converges.
(d) If (sn) and (sntn) are convergent sequences, then (tn) converges.
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