A binary operator: A implies B is false only when A is true and B is false.
Material implication
Related concepts
- Logical disjunction (OR)
- Logical negation (NOT)
- Biconditional (IFF)
- Modus ponens
- Principle of mathematical induction
- Converse of a conditional
- Inverse of a conditional
- Contrapositive of a conditional
- Implication-as-disjunction equivalence
- Contrapositive equivalence
- Biconditional decomposition
- Modus tollens
- Hypothetical syllogism
- Sufficient condition
- Necessary condition
- Argument (deductive)
- Affirming the consequent (fallacy)
- Denying the antecedent (fallacy)
- Sequent calculus