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

  • $p$: True (T).
  • $q$: False (F).
  • $r$: 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

Relation to other Axioms

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