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.
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Vinony's link graph records 142 inbound references to contraposition, and connects out to semantic theory of truth, mathematical logic and commutative property.
It sits within the topics Mathematical logic and Theorems in propositional logic.
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- Contraposition
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Encyclopedic overview
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 .
Excerpted from Wikipedia’s “contraposition” article, available under the CC BY-SA 4.0 licence.