The union of two sets 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.

more lengthy explanation for Math 2 level

Examples

$R^{-} \cup R^{+} \cup {0} = R$ (In other words, the union of the negative reals, the positive reals and zero make up all of the real numbers.)