001 Commutative Laws in Logic
Commutative Equivalences in Logic
\[p \wedge q \equiv q \wedge p,\]
\[p \vee q \equiv q \vee p.\]
Examples
Let p: "The number \(n\) is natural.", and 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 |