Set operation (Union)

The union of sets $A$ and $B$, $A\cup B$, is the set $$ A \cup B = \{ x | x \in A \text{ (inclusive)} \text{ or } x \in B \} $$

$A\cup B$ consists of elements in either $A$ or $B$ or both.

Venn diagram of $A\cup B$

For example, let $A=\{4,7,8\}$ and $B=\{10,4,9\}$. Hence, $A\cup B=\{4,7,8,9,10\}$.

Properties of union

• Identity law (Sets)

  The identity law is that $A\cup \varnothing =$ $A$.

  Link to original

• $A\subseteq B⟺A\cup B=B$