Enumerable disjoint subsets whose union is equal to the union of the sets I'm given that two sets, $A$ and $B$ are enumerable. I have to show that there exist subsets $A \supset C$ and $B \supset D$ ($C$ and $D$ also enumerable) such that $C$ and $D$ are disjoint and $A\cup B = C \cup D$. I was thinking to take $A=B=\{0,1\}$ and define $C=\{n : f(n)=1\}$, $D=\{n: f(n)=0\}$. 
Do you think this is right?
This answer assumes that enumerable means recursively enumerable.

Here is an enumerator for $C$:


Run enumerators for $A,B$ in parallel.
Whenever the enumerator for $A$ outputs a word, check whether the word has already been enumerated by the enumerator for $B$; if it hasn't, output it and continue.


The enumerator for $D$ is defined symmetrically.