Question

Let (an) and (bn) be two nonnegative sequences.
Let cn =max{an,bn} for each n∈N.
Prove the following statements or give a counterexample when false.
(a) If (an) and (bn) converge, so does (cn).
(b) If (an) and (bn) diverge, so does (cn).
(c) If the summation of an and the summation of bn converge, so does the summation of cn.
(d) If the summation of an and the summation of bn diverge, so does the summation of cn.