contrapositive: meaning, definition, pronunciation and examples
LowFormal, Academic, Technical
Quick answer
What does “contrapositive” mean?
In logic, a proposition derived from another by negating both the subject and predicate and then reversing their order. The logical equivalent of an original conditional statement.
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Pronunciation
Definition
Meaning and Definition
In logic, a proposition derived from another by negating both the subject and predicate and then reversing their order. The logical equivalent of an original conditional statement.
A statement that takes an opposing or countering position; something that is the direct opposite or converse of a given principle, argument, or situation. Can be used more broadly in rhetoric or argumentation to denote a directly opposing viewpoint.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. The term is equally technical in both variants.
Connotations
Exclusively academic and logical. No cultural or evaluative connotations beyond its technical precision.
Frequency
Extremely low frequency in general corpora, appearing almost exclusively in academic texts on logic, mathematics, philosophy, or computer science. Frequency is identical between UK and US academic contexts.
Grammar
How to Use “contrapositive” in a Sentence
the contrapositive of [noun phrase]to form the contrapositive of [statement][statement] and its contrapositive are logically equivalentVocabulary
Collocations
Examples
Examples of “contrapositive” in a Sentence
adjective
British English
- The contrapositive form of the theorem is often easier to prove.
- She presented a contrapositive argument to deconstruct the assumption.
American English
- The contrapositive statement provided a clearer path for the proof.
- His approach was purely contrapositive reasoning.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core term in logic, mathematics, philosophy, and computer science proofs. Used to describe a method of proof (proof by contrapositive).
Everyday
Extremely rare. Would only be used in highly educated discussion about argument structure.
Technical
Precise term in formal systems, symbolic logic, theorem proving, and programming (e.g., conditionals in code).
Vocabulary
Synonyms of “contrapositive”
Strong
Neutral
Weak
Vocabulary
Antonyms of “contrapositive”
Watch out
Common Mistakes When Using “contrapositive”
- Using it to mean simply 'opposite' without the logical structure of negation-and-reversal.
- Confusing it with 'converse' or 'inverse'.
- Using it in informal contexts where it will not be understood.
- Misspelling as 'contra-positiv' or 'contraposative'.
FAQ
Frequently Asked Questions
Yes, in classical logic, a conditional statement and its contrapositive are always logically equivalent. This is the foundation of 'proof by contrapositive.'
For 'If P then Q': Converse is 'If Q then P'. Inverse is 'If not-P then not-Q'. Contrapositive is 'If not-Q then not-P'. Only the contrapositive is logically equivalent to the original.
Primarily it is a noun ('the contrapositive'). It can be used attributively as an adjective (e.g., 'contrapositive proof'), but it is not used predicatively ('the proof is contrapositive' is less common).
It is fundamental in mathematics (especially proofs), formal logic, philosophy (logic), computer science (algorithm correctness, Boolean logic), and to some extent in linguistics (semantic entailment).
In logic, a proposition derived from another by negating both the subject and predicate and then reversing their order. The logical equivalent of an original conditional statement.
Contrapositive is usually formal, academic, technical in register.
Contrapositive: in British English it is pronounced /ˌkɒn.trəˈpɒz.ɪ.tɪv/, and in American English it is pronounced /ˌkɑːn.trəˈpɑː.zə.t̬ɪv/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[None directly associated with the term]”
Learning
Memory Aids
Mnemonic
Think 'CONTRARY POSITION': You CONTRAdict the original statement and then rePOSITION the elements (swap them). First, make both parts negative, then flip their order.
Conceptual Metaphor
LOGICAL EQUIVALENCE IS MIRRORING/REFLECTING (with a negation filter).
Practice
Quiz
Which of the following is the contrapositive of 'If it is raining, then the ground is wet'?