002 Associative Laws in Logic
Associative Equivalences in Logic
\[(p \wedge q) \wedge r \equiv p \wedge (q \wedge r),\]
\[(p \vee q) \vee r \equiv p \vee (q \vee r).\]
Examples
Let p: True (T), q: False (F), and r: True (T).
Conjunction
(T and F) and T \(=\) F and T \(=\) F, which is logically equivalent to: T and (F and T) \(=\) T and F \(=\) F.
Disjunction
(T or F) or T \(=\) T or T \(=\) T, which is logically equivalent to: T or (F or T) \(=\) T or T \(=\) T.
Meaning of the used symbols
| Symbol | Meaning |
|---|---|
| \(\wedge\) | and |
| \(\vee\) | (not exclusive) or |
| \(\equiv\) | is logically equivalent to |