Show that for A and B, a language J exists such that A $\leq_T$ J, B $\leq_T$ J
Just define $J$ as $A\oplus B = \{m \mid m =2k \text{ if } k \in A, \text{ and }  m =2k+1 \text{ if } k \in B \}$. Then $k \in A$ is decided by querying $2k \in A\oplus B$, and $k \in B$ is decided by querying $2k+1 \in A\oplus B$. Thus $A \leq_T A\oplus B$, $B \leq_T A\oplus B$. 

This result is well known in the theory of computability. It establishes the least upper bound on the lattice of the Turing degrees of $A$ and $B$.