I'm studying for my final in theory of computation, and I'm struggling with the proper way of answering whether this statement is true of false.
By the definition of $\leq_m$ we can construct the following statement,
$w \in A \iff f(w) \in B \rightarrow w \notin A \iff f(w) \notin B$
This is where I'm stuck, I want to say that since we have such computable function $f$ then it'll only give us the mapping from A to B if there is one, otherwise it wont.
I don't know how to phrase this correctly, or if I'm even on the right track.