In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent...

criticized in the phrase: absence of evidence is not evidence of absence. Contraposition is a logically valid rule of inference that allows the creation of a...

argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. The form of a modus tollens argument is...

a categorical statement. Note that this contraposition in the traditional logic is not same to contraposition (also called transposition) in the modern...

inference.[citation needed] Modus ponens Conditional proof Classical contraposition Classical reductio ad absurdum Unlike the semantic definition, this...

is often used instead of "proof by mathematical induction". Proof by contraposition infers the statement "if p then q" by establishing the logically equivalent...

as logic and mathematics. Appeal to ridicule Argument from fallacy Contraposition List of Latin phrases Mathematical proof Prasangika Slippery slope Strawman...

smaller series, Σ a n {\displaystyle \Sigma a_{n}} must converge. By contraposition, if the red series Σ a n {\displaystyle \Sigma a_{n}} is proven to diverge...

inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical...

ever-changing waters flowing through it, and all things exist as a contraposition of opposites. According to Diogenes Laertius, Plato received these ideas...

C=ND(N\otimes N)} In the classical propositional calculus, the law of contraposition p → q ≡ ¬q → ¬p is proved because the equivalence holds for all the...

Syntactically, (1) and (2) are derivable from each other via the rules of contraposition and double negation. Semantically, (1) and (2) are true in exactly the...

existence or non-existence. Argument from ignorance Argument from silence Contraposition Probatio diabolica Proof by exhaustion "Absence of Evidence Is Not Evidence...

potentially habitable worlds are. The Hart-Tipler conjecture is a form of contraposition which states that because no interstellar probes have been detected...

directions of implication, Bayes' theorem represents a generalization of the contraposition law, which in classical propositional logic can be expressed as: ( B...

for the second problem, one exists for the first problem as well. By contraposition, if no efficient algorithm exists for the first problem, none exists...

cities, including Castelfranco Veneto (founded by the Trevigiani in contraposition to Padua), had become attractive to neighbouring powers, including the...

(grammatical polarity) Ampheck Apophasis Binary opposition Bitwise NOT Contraposition Cyclic negation Negation as failure NOT gate Plato's beard Square of...

category theory, the term conglomerate is applied to arbitrary sets as a contraposition to the distinguished sets that are elements of a Grothendieck universe...

then not-B implies not-A", and vice versa), which expresses the law of contraposition. For instance, "If it's a book, it is blue; if it's not blue, it's not...

(2a − 1)((2a)b−1 + (2a)b−2 + ... + 2a + 1) so 2p − 1 is composite. By contraposition, if 2p − 1 is prime then p is prime. If p is an odd prime, then every...

Scuola romana or Scuola di via Cavour was a 20th-century art movement defined by a group of painters within Expressionism and active in Rome between 1928...

and P cannot be swapped in All S are P. Philosophy portal Aristotle Contraposition Inverse (logic) Logical connective Obversion Term logic Transposition...

for lunch, then Sam also cannot have eaten an orange for lunch (by contraposition). However, merely saying that Sam did not eat an orange for lunch provides...

cannot be true unless Q is true" or "if Q is false, then P is false". By contraposition, this is the same thing as "whenever P is true, so is Q". The logical...

foreigner like Sapp against a Japanese national like Taro, a cultural contraposition, also gained comparisons with Japanese professional wrestling legend...

can be expressed as: If something is a raven, then it is black. Via contraposition, this statement is equivalent to: (2) If something is not black, then...

each according to his ability, to each according to his deeds". In contraposition, the anarcho-communists (such as Peter Kropotkin, Carlo Cafiero and...

these statements, it might appear one could make these deductions by contraposition and conditional disjunction: ([a] from [ii]) If Yog was white, then...

concept popularized by Carl Gustav Jung. The Age of Aquarius was seen in contraposition with current the Age of Pisces: whereas the Age of Pisces represents...