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

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

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...

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...

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...

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...

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

distinct elements; that is, x1 ≠ x2 implies f(x1) ≠ f(x2) (equivalently by contraposition, f(x1) = f(x2) implies x1 = x2). In other words, every element of the...

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...

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

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...

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

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...

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

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...

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...

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

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

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

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...

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

(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...

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

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

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

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...

the law of excluded middle implies a proposition, then by applying contraposition twice and using the double-negated excluded middle, one may prove double-negated...

non-P". "All S are not P" (E form) becomes "Some non-S are not non-P". Contraposition Converse (logic) Obversion Transposition (logic) Taylor, Courtney K...