The question has some redundant data.
It is given $A$ and $B$ are disjoint. So, $A \cap B = \emptyset \implies A' \cup B' = \Sigma^*$ which is regular (and hence r.e. also). So, "Let $A' \cup B'$ also be recursive enumerable" is not necessary in question.
Now, I say option A is true which implies options B and C are false as option A says both $A$ and $B$ can be non r.e. Example for such an $A$ and $B$ is given below..
$A = L_1 = \{\langle M,w,0 \rangle \mid M \text{ halts on } w\}$
$B = L_2 = \{\langle M,w,1 \rangle \mid M \text{ halts on } w\}$
Here $L_1$ and $L_2$ (variants of halting problem) are r.e. and neither is recursive. The last bit is added to ensure $L_1 \cap L_2 = \emptyset$.