contraposition
Sign in to saveIn logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as . The contrapositive of a statement has its antecedent and consequent negated and swapped.
Article
29 sectionsContents
- Intuitive explanation
- Formal definition
- Sequent notation
- Proofs
- Simple proof by definition of a conditional
- Simple proof by contradiction
- More rigorous proof of the equivalence of contrapositives
- In classical propositional calculus system
- Comparisons
- Examples
- Truth
- Traditional logic
- Form of transposition
- Sufficient condition
- Necessary condition
- Necessity and sufficiency example
- Relationship of propositions
- Distinguished from transposition
- Proof by contrapositive
- Difference with proof by contradiction
- Example
- In nonclassical logics
- Intuitionistic logic
- Subjective logic
- In probability theory
- See also
- References
- Sources
- External links
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as . The contrapositive of a statement has its antecedent and consequent negated and swapped.
Conditional statement P \rightarrow Q. In formulas: the contrapositive of P \rightarrow Q is \neg Q \rightarrow \neg P .