Associative Laws in Set Theory
Associative Properties in Set Theory
\[(A \cup B) \cup C = A \cup (B \cup C)\] \[(A \cap B) \cap C = A \cap (B \cap C).\]Examples
Let set $A = \{1, 2\}$, set $B = \{2, 3\}$, and set $C=\{2, 4\}$.
| Union |
|---|
| $(A \cup B) \cup C = A \cup (B \cup C) = \{1, 2, 3, 4\}$ |
| Intersection |
|---|
| $(A \cap B) \cap C = A \cap (B \cap C) = \{2\}$ |
Meaning of the used symbols
| Symbol | Meaning |
|---|---|
| $ \{ \} $ | set |
| $ \cup $ | union of sets |
| $ \cap $ | intersection of sets |