Example · Undergraduate
Terms
| Term | This example | Why |
|---|
| propositional formula |
✓ |
$p \lor \neg p$ is a propositional formula, because $p \lor \neg p$ is built from the propositional variable $p$ with the connectives $\lor$ and $\neg$.
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| proposition |
✗ |
$p \lor \neg p$ is not a proposition, although $p \lor \neg p$ is true for every truth value of $p$: the formula is a pattern, and each substitution of a proposition for $p$, such as “$7$ is prime or $7$ is not prime,” gives a different proposition.
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Distinctions using this example
- Proposition vs. propositional formula: The tautology $p \lor \neg p$ is true for every truth value of $p$, but $p \lor \neg p$ is still a formula, not a proposition, because $p \lor \neg p$ says nothing about a particular statement until $p$ is replaced.
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