The union of two sets contains everything in either set. If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}. Common elements are listed once. The symbol is ∪.

In Venn diagrams, the union is the entire shaded region covered by both circles. In probability, the union of two events is the event that at least one occurs. The addition rule for probabilities involves the union.

Union appears in set theory, logic, databases, and programming. In SQL, the UNION operator combines results from two queries. In mathematics, union is one of the basic set operations, along with intersection and complement. The concept is simple but widely used.

• Set of all elements in either set
• Symbol: ∪
• Common elements listed once
• Used in probability, databases, and logic