I am working on theory of computation problems, and I came across this one:
Show that for A and B, a language J exists such that $A \leq_T J$, $B \leq_T J$
The only $J$ I can think of for the moment is the language that uses a $TM$ $N$ which contains a recognizer $M1$ for $A$, and another recognizer $M2$ for $B$. $N$ uses oracle $J$ to check if input $x\in A U B$. If $J$ accepts, then it means that either $M1$ or $M2$ will halt, so $N$ can now simultate $M1$ and $M2$ simultaneously.
But I think there should be a simpler way to solve this..... any help?