The union of two sets $A$ and $B$, denoted $A \cup B$, is the set of things which are either in $A$ or in $B$ or both.

illustration of the output of the union operation

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

$$x \in C \leftrightarrow (x \in A \lor x \in B)$$

That is, Iff $x$ is in the union $C$, then either $x$ is in $A$ or $B$ or possibly both.

todo: more lengthy explanation for Math 2 level

Examples

$\{1,2\} \cup \{2,3\} = \{1,2,3\}$
$\{1,2\} \cup \{8,9\} = \{1,2,8,9\}$
$\{0,2,4,6\} \cup \{3,4,5,6\} = \{0,2,3,4,5,6\}$
$\mathbb{R^-} \cup \mathbb{R^+} \cup \{0\} = \mathbb{R}$ (In other words, the union of the negative reals, the positive reals and zero make up all of the real numbers.)

Union