Relative complement

The relative complement of two sets $A$ and $B$, denoted $A \setminus B$, is the set of elements that are in $A$ while not in $B$.

Formally stated, where $C = A \setminus B$

$$x \in C \leftrightarrow (x \in A \land x \notin B)$$

That is, Iff $x$ is in the relative complement $C$, then $x$ is in $A$ and x is not in $B$.

For example,

• $\{1,2,3\} \setminus \{2\} = \{1,3\}$
• $\{1,2,3\} \setminus \{9\} = \{1,2,3\}$
• $\{1,2\} \setminus \{1,2,3,4\} = \{\}$

If we name the set $U$ as the set of all things, then we can define the Absolute complement of the set $A$, $A^\complement$, as $U \setminus A$