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 $C=A\setminus B$

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

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

For example,

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

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 $U\setminus A$