The union of two sets includes all elements from both sets, without duplication. It is denoted by the symbol ∪. The union operation forms a set that contains all elements that are in set A, in set B, or in both.
\[ A \cup B = \{x \mid x \in A \text{ or } x \in B\} \]
This means the set of all elements x such that x is in A, or in B, or in both.
Let:
\[ A = \{2, 4, 6\}, \quad B = \{4, 5, 7\} \] \[ A \cup B = \{2, 4, 5, 6, 7\} \]
Note that 4, being common in both sets, appears only once in the union.