The question is whether the following statement is true or false:
$A \leq_T B \implies A \leq_m B$
I know that if $A \leq_T B$ then there is an oracle which can decide A relative to B. I know that this is not enough to say that there is a computable function from A to B that can satisfy the reduction.
I don't know how to word this in the proper way or if what I'm saying is enough to say that the statement is false. How would I go about showing this?
EDIT: This is not a homework problem per se, I'm reviewing for a test. Where $\leq_T$ is Turing reducibility, and $\leq_m$ is mapping reducibility.