UNION

Definition

The union of two or more sets is a set containing all elements from the included sets without duplication. It is typically denoted by the symbol $\cup$.

5 Must Know Facts For Your Next Test

1. The union of sets A and B, denoted as $A \cup B$, includes all elements that are in A, in B, or in both.
2. In Venn diagrams, the union of sets is represented by the area covered by all included sets.
3. For any set A, the union with itself ($A \cup A$) equals A.
4. The union operation is commutative: $A \cup B = B \cup A$.
5. The union operation is associative: $(A \cup B) \cup C = A \cup (B \cup C)$.

Review Questions

• How do you represent the union of two sets in notation?
• What does the union of two sets include?
• Is the union operation commutative and associative? Provide an example.

Related terms

Intersection:

The intersection of two or more sets is a set containing only the elements common to all included sets. Denoted by $\cap$.

Complement:

The complement of a set A includes all elements not in A. It is usually denoted by $A^c$ or $\overline{A}$.

Disjoint Sets:

Two or more sets are disjoint if they have no elements in common. Their intersection is an empty set.