Set difference

Definition

Let $A$ and $B$ be sets. The set difference of $A$ and $B$ is the set $$A \setminus B = \{x \in A \mid x \notin B\}.$$ It is also called the relative complement of $B$ in $A$.

Remarks

Another notation is $A - B$. Example: $\{1, 2, 3\} \setminus \{2, 4\} = \{1, 3\}$. The set $B$ need not be a subset of $A$. In general, $A \setminus B \neq B \setminus A$.

Explanations

L1 human

To compute $A \setminus B$, start with $A$ and remove each element that is also in $B$. Elements of $B$ that are not in $A$ do not matter.