False consider,

s_n=1,0,1,0,1,0,...

t_n=-1,0,-1,0,-1,0,...

False consider,B) If (Sn) and (Tn) are divergent sequences, then (SnTn) diverges

s_n=t_n=(-1)^n/n

If {s_n} converges and {s_n+t_n} convergesn then by theorems we have that,C) If (Sn) and (Sn + Tn) are convergent sequences, then (Tn) converges

{s_n+t_n}-{s_n}={t_n} converges.

No.D) If (Sn) and (SnTn) are convergent sequences, then (Tn) converges

If s_n does not converges to zero then this is true.

But sometimes no.

Let s_n=0 and t_n=n.