Union
Definition
The union of two sets \(A\) and \(B\), written \(A \cup B\), is the set of all elements that are in \(A\) or in \(B\) (or in both).
\[A \cup B = \{x : x \in A \lor x \in B\}\]
Properties
Commutativity
\[A \cup B = B \cup A\]
Associativity
\[(A \cup B) \cup C = A \cup (B \cup C)\]
Identity
\[A \cup \emptyset = A\]
Idempotence
\[A \cup A = A\]
Examples
Example 1
\[\{1, 2\} \cup \{2, 3\} = \{1, 2, 3\}\]
Example 2
\[\{a, b\} \cup \{c, d\} = \{a, b, c, d\}\]
Related
- Set
- Intersection — Common elements
- Complement
Backlinks
No other pages link here yet.