002 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 |