contrapositive
Negated, flipped conditional
The contrapositive is a logical transformation of a conditional statement: if "A implies B," the contrapositive is "not-B implies not-A." Both statements are logically equivalent—one is true if and only if the other is.
If it's raining then the ground is wet has the contrapositive If the ground isn't wet then it isn't raining.
The contrapositive is fundamental in mathematical proofs.
Denial or cancellation
- implicationIndirect suggestion or consequence
- conditionalDependent on prerequisites
- contradictionOpposing claims, incompatible together
- counterexampleInstance disproving a claim
disproof · validity · soundness · inference · indirect proof · reductio ad absurdum · assumption · QED
Indirect suggestion or consequence
- negationDenial or cancellation
- antecedentSomething that precedes
- consequentFollowing as an effect
- conditionalDependent on prerequisites
biconditional · truth table · quantifiers · universal · existential · validity · soundness · contradiction
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- inverseOpposite in position
- negationDenial or cancellation
- reversalComplete change of direction
- transpositionSwapping positions of elements
equivalent · swap · flip · antecedent · consequent · restatement · reformulation · if-then
Error in reasoning
- invalidWithout legal force
- non sequiturIllogical conclusion or remark
- logical errorFlaw in reasoning
- confusionMental disorientation or bewilderment
negation
Denial or cancellation
- implicationIndirect suggestion or consequence
- conditionalDependent on prerequisites
- contradictionOpposing claims, incompatible together
counterexample · disproof · validity · soundness · inference · indirect proof · reductio ad absurdum · assumption · QED · demonstration
implication
Indirect suggestion or consequence
- negationDenial or cancellation
- antecedentSomething that precedes
- consequentFollowing as an effect
conditional · biconditional · truth table · quantifiers · universal · existential · validity · soundness · contradiction · tautology
converse
Engage in dialogue
transposition · equivalent · swap · flip · antecedent · consequent · restatement · reformulation · if-then
fallacy
Error in reasoning
- invalidWithout legal force
- non sequiturIllogical conclusion or remark
- logical errorFlaw in reasoning
- logicpremise, premises, conclusion, conclusions, inference
- Propositionsstatement, assertion, claim, premise, conclusion
- proofsproof by contradiction, contradiction, theorem, lemma, corollary
- oppositesopposites, antonym, antonyms, inverse, converse
- Dualityduality, dual nature, two sides, yin and yang, yin-yang
contrapositiveconverse
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inverse · obverse · logical fallacy · affirmative · conditional