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