Yes, there is. Let $A\;\triangle\; B$ denote the symmetric difference of the sets $A$ and $B$. Given an object $x$, $x\in A\;\triangle\; B\iff (x\in A)\text{ XOR }(x\in B).$ In general, one has a correspondence between statements in set theory and statements in logic, e.g. $x\in A\cup B\iff (x\in A)\text{ OR }(x\in B)$ $x\in A\cap B\iff (x\in A)\text{ AND }(x\in B)$ $x\in A^c\iff\text{NOT }(x\in A)$
So, for example, $A\setminus B=A\cap B^c$, so $x\in A\setminus B\iff x\in A\cap B^c\iff(x\in A)\text{ AND }(x\in B^c)\iff (x\in A)\text{ AND }(\text{NOT }(x\in B))$