how do I prove that for every 2 languages $A,B\in R$ where $A,B \notin \{ \emptyset , \Sigma^* \}$
I can do a reduction $A \leq_m B$?
[EDIT] My try:
$A$ is decidable therefore it has a turing machine that decides it - $T_A$
For every x, we can check whether $T_A$ accepts x or not, if it accepts then we run over the alphabet and try to find words that are in B.
$B \notin \{ \emptyset , \Sigma^* \}$ therefore there exists words that are in B and words that are not.
if $T_A$ accepts x then we return a word that we found that is in B else if x is not in A then we return a word that is not in B.
This can be done only because $A,B \notin \{ \emptyset , \Sigma^* \}$ And because A and B are decidable
