The union of two sets \(A\) and \(B\) is the set of all elements that are in the set \(A\) or in the set \(B\), or in both.

We use the symbol \(\cup\) to say that we're taking a union.

For example, the Venn diagram in the picture shows the sets \(\text{Rugby} = \{\text{Ben}, \text{Jacob}, \text{Ed}, \text{Al}\}\) and \(\text{AFL} = \{\text{Ed}, \text{Al}, \text{Sam}, \text{Tom}\}\). Their union is \(\text{Rugby} \cup \text{AFL} = \{\text{Ben},\text{Jacob},\text{Ed},\text{Al}, \text{Sam}, \text{Tom}\}\).