What Are Rules of Inference?

Rules of inference are like the rules of the game for making valid logical arguments. They allow us to move from premises to conclusions step by step.

Common Rules

• Modus Ponens: If \( p \rightarrow q \) and \( p \), then \( q \).
• Modus Tollens: If \( p \rightarrow q \) and \( \lnot q \), then \( \lnot p \).
• Disjunctive Syllogism: If \( p \lor q \) and \( \lnot p \), then \( q \).
• Hypothetical Syllogism: If \( p \rightarrow q \) and \( q \rightarrow r \), then \( p \rightarrow r \).

Applying Rules

By applying these rules correctly, you can build solid arguments and spot errors in reasoning.

Practice with Proofs

Logical proofs use these rules in sequence to show that a conclusion must be true if the premises are true.