Distributive Equivalences in Logic

\[p \vee (q \wedge r) \equiv (p \vee q) \wedge (p \vee r)\] \[p \wedge (q \vee r) \equiv (p \wedge q) \vee (p \wedge r).\]

Examples

  • $p$: True (T).
  • $q$: False (F).
  • $r$: True (T).
Conjunction
T or (F and T) $=$ T, which is logically equivalent to: (T or F) and (T or T) $=$ T.
Disjunction
T and (F or T) = T, which is logically equivalent to: (T and F) or (T and T) = T.

Meaning of the used symbols

Symbol Meaning
$ \wedge $ and
$ \equiv $ is logically equivalent to
$ \vee $ (not exclusive) or

Relation to other Axioms

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