contrapositives
Negated inverse statements
Contrapositives are logically equivalent restatements formed by negating and reversing a conditional statement.
If the original claim is "all dogs are mammals," the contrapositive is "all non-mammals are non-dogs"—and both are equally true or false.
The contrapositive of "if it rains, the ground gets wet" is "if the ground isn't wet, it didn't rain." The term belongs to formal logic and mathematics, where proving a contrapositive often proves the original statement more easily.
Dependent on prerequisites
- antecedentSomething that precedes
- consequentFollowing as an effect
- implicationIndirect suggestion or consequence
- negationDenial or cancellation
if-then · truth-value · biconditional · inverse · converse · obverse
Demonstrated logical conclusion
- lemmaBase form, or helper theorem
- corollaryLogical natural consequence
- axiomSelf-evident starting principle
- postulateAssumed starting point
conjecture · proof · implication · equivalence · quantifier
Formal deductive argument structure
- premiseFoundation for logical argument
- conclusionEnd or deduction
- inferenceConclusion reached through reasoning
- categoricalUnconditional and explicit
deduction · universal · particular · affirmative · negative · conversion
Disproof via contradiction
- validityQuality of being sound
- soundnessReliability of structure
- derivationSource or origin tracing
- demonstrationPublic display of opinion
conditional
Dependent on prerequisites
- antecedentSomething that precedes
- consequentFollowing as an effect
- implicationIndirect suggestion or consequence
negation · if-then · truth-value · biconditional · inverse · converse · obverse
theorem
Demonstrated logical conclusion
- lemmaBase form, or helper theorem
- corollaryLogical natural consequence
- axiomSelf-evident starting principle
postulate · conjecture · proof · implication · equivalence · quantifier
syllogism
Formal deductive argument structure
- premiseFoundation for logical argument
- conclusionEnd or deduction
- inferenceConclusion reached through reasoning
categorical · deduction · universal · particular · affirmative · negative · conversion
reductio
Disproof via contradiction
- validityQuality of being sound
- soundnessReliability of structure
- derivationSource or origin tracing
demonstration · falsification · refutation · disproof · counterexample
contrapositivesconverses
Speaks with another
inverses · obverses · fallacies · logical fallacies · non-sequiturs