The Boolean Logic of Set Differences

The set difference between two sets $A$ and $B$ consists of all elements of $A$ that are not elements of $B$. It is written $A \setminus B$ or $A - B$.

Note that unlike the union and intersection operations, the set difference operation is not commutative! That is, $A \setminus B$ and $B \setminus A$ are not the same thing.

Something to consider: what is $B \setminus A$?

Unless $A = B$ (they have the same exact elements to begin with), the set differences $A\setminus B$ and $B\setminus A$ always differ by at least one element: either $A$ has something not in $B$, or $B$ has something not in $A$.