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