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.

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.)