**Modus Tollens** is a rule of inference in propositional logic that states that if we have a Material Condtional that has a false consequent, then we may infer the negation of the antecedent. In other words, if P implies Q is true and Q is false, then we may infer that P is false. In rule form, this is often expressed as

**Rules of inference**

Modus Ponens | **Modus Tollens** | Disjunctive Syllogism | Hypothetical Syllogism | Conjunction Introduction | Conjunction Elimination | Disjunction Introduction | Disjunction Elimination | Bicondional Introduction | Biconditional Elimination | Constructive Dilemma | Destructive Dilemma | Absorption | Modus ponendo tollens

**Rules of Transformation**

Double Negation | Associative property | Commutative property | Distributive property | DeMorgan's Laws | Tautology | Exportation | Material Implication | Transposition