| Precedence | Operator | Description |
|---|---|---|
| 1 | Negation (!) | Unary logical negation |
| 2 | Conjunction (&&) | Logical AND |
| 3 | Disjunction (||) | Logical OR |
| 4 | Implication (→) | Logical implication |
| 5 | Biconditional (↔) | Logical biconditional |
In propositional logic, the sequence of precedence determines the order in which logical operations are evaluated in an expression. Operators with higher precedence are evaluated before those with lower precedence. Here’s the explanation:
- Negation (!): Unary logical negation is evaluated first. It flips the truth value of a proposition.
- Conjunction (&&): Logical AND is evaluated next. It returns true only if both operands are true.
- Disjunction (||): Logical OR is evaluated after conjunction. It returns true if at least one of the operands is true.
- Implication (→): Logical implication is evaluated next. It evaluates to false only when the antecedent is true and the consequent is false.
- Biconditional (↔): Logical biconditional is evaluated last. It evaluates to true if both operands have the same truth value.