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

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

technical issues, or some kind of oversight from the hiring team. 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...

ever-changing waters flowing through it, and all things exist as a contraposition of opposites, while Parmenides adopted an altogether contrary vision...

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...

comes with music co-written by Luis F. Ochoa and includes an intriguing contraposition of rock guitars and Latin brass, utilized among other seemingly disparate...

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...

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...

its codomain; 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...

conjecture might also simultaneously prove Fermat's Last Theorem. By contraposition, a disproof or refutation of Fermat's Last Theorem would disprove the...

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...

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

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...

who adopted a laissez-faire system he termed anarchistic socialism in contraposition to state socialism. This tradition has been recently associated with...

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...

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

treacherous tyrant who serves as a nemesis to Liu Bei, often depicted in contraposition as a hero trying to revive the declining Han dynasty. During the Ming...

the final hours, leaving Soviet Foreign Minister Dmitri Shepilov in contraposition. Why is that we have never heard voices in connection with the freedom...

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...

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...

(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...

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

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

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...

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

implies that the variance is constant for all treatments. Therefore, by contraposition, a necessary condition for unit-treatment additivity is that the variance...