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.

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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.)