Commutative Equivalences in Logic

\[p \wedge q \equiv q \wedge p\] \[p \vee q \equiv q \vee p.\]

Examples

  • $p$: “The number $n$ is natural.”
  • $q$: “The number $n$ is even.”
Conjunction
“The number $n$ is natural and even” is logically equivalent to “The number $n$ is even and natural.”
Disjunction
“The number $n$ is natural or even” is logically equivalent to “The number $n$ is even or natural.”

Meaning of the used symbols

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

Relation to other Axioms

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