Show that a set is turing reducible to another set
The definition of Turing reducible, is that there exists a Turing reduction - an algorithm for $A+B$ that uses an oracle to $A$.
To understand this, you must first understand oracle machines. Those machines, are like turing machines, but can ask an &quot;oracle&quot; whether any $x$ is in $A$ or not, and would get an answer in $O(1)$, regardless of what $A$ is (doesn't even matter if it is not decidable!)
So, a turing reduction basically means that if you know for any $x$ whether its in $A$ or not in $A$, then you can decide whether a given $x$ is in $A+B$. Formally, this statement can be written as ${(A+B)}^A\in R$.
So basically the question asks you to show that ${(A+B)}^A,{(A+B)}^B\in R$