Law of denying the consequent

Definition

The law of denying the consequent (also called modus tollens) is a valid form of argument in propositional logic. It states that if 'P implies Q' and 'Q is false,' then 'P must also be false.'

5 Must Know Facts For Your Next Test

1. Modus tollens follows the structure: If P, then Q. Not Q. Therefore, not P.
2. It is one of the fundamental rules of inference in classical logic.
3. Modus tollens can be symbolically represented as: (P → Q), ¬Q ⊢ ¬P.
4. The validity of modus tollens relies on the logical consistency between premises and conclusion.
5. Modus tollens can be used to disprove hypotheses by showing their consequences are false.

Review Questions

• What is the symbolic representation of modus tollens?
• How does denying the consequent help in disproving hypotheses?
• What are the premises and conclusion in a modus tollens argument?

Related terms

Modus Ponens: A form of argument where from 'If P, then Q' and 'P is true,' it concludes 'Q must also be true.'

Contrapositive: The statement formed by negating and swapping both terms of an implication, i.e., from 'If P, then Q' to 'If not Q, then not P.'

Inference Rule: A logical rule that outlines how new statements can be derived from existing statements within a formal system.