“$7$ is prime and $4$ is not prime”
This statement is the result of substituting “$7$ is prime” for $p$ and “$4$ is prime” for $q$ in the propositional formula $p \land \neg q$.
Terms
| Term | This example | Why |
|---|---|---|
| proposition | ✓ | “$7$ is prime and $4$ is not prime” is a proposition, because the statement is true: $7$ is prime, and $4$ is not prime. |
| propositional formula | ✗ | “$7$ is prime and $4$ is not prime” is not a propositional formula, because the statement contains no propositional variables; the statement is one instance of the formula $p \land \neg q$. |
Distinctions using this example
- Proposition vs. propositional formula: Substituting “$7$ is prime” for $p$ and “$4$ is prime” for $q$ in the formula $p \land \neg q$ gives the proposition “$7$ is prime and $4$ is not prime,” which is true.