How can I prove that a function F isn't a pseudo random function?
your title asks "How to prove that a function F isn't a pseudo random function", in your question case (b) is not PRF which is easy to prove. function $F'$ is PRF if for all PPT distingushers $D$, success probability of $D$ distinguishing $F'$ from random function be negligible. So for proving that function $F'$ is not PRF it suffices to construct one distinguisher (which queries to its oracle and look for non-random patterns) with non-negligible success probability.

In contrast case (a) here is PRF, which is harder to proof. for proving function $F'$ is PRF as @fkraiem mentioned suppose $F'$ is not PRF and $D'$ is distinguisher for $F'$ then construct an algorithm $A$ which breaks some assumption (Distingush $F$ from random function here breaks assumption of $F$ being PRF).