Let a n and b n be series with positive terms. Is each of the following statements

Let Σa_n and Σb_n be series with positive terms. Is each of the following statements true or false? If the statement is false, give an example that disproves the statement.

(a) If Σa_n and Σb_n are divergent, then Σa_nb_n is divergent.

(b) If Σa_n converges and Σb_n diverges, then Σa_nb_n diverges.

(c) If Σa_n and Σb_n are convergent, then Σanb_n is convergent.