Decide which of the following statements are true and which are false. Prove the true ones and

Question:

Decide which of the following statements are true and which are false. Prove the true ones and provide a counterexample for the false ones.
a) If xn converges, then xn/n also converges.
b) If xn does not converge, then xn/n does not converge.
c) If xn converges and yn is bounded, then xny converges.
d) If xn converges to zero and yn > 0 for all n ∊ N, then xnyn converges.