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Contraposition. In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
Affirming the consequent is the action of taking a true statement and invalidly concluding its converse . The name affirming the consequent derives from using the consequent, Q, of , to conclude the antecedent P. This fallacy can be summarized formally as or, alternatively, . [5]
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
A system will be said to be inconsistent if it yields the assertion of the unmodified variable p [S in the Newman and Nagel examples]. In other words, the notion of "contradiction" can be dispensed when constructing a proof of consistency; what replaces it is the notion of "mutually exclusive and exhaustive" classes.
Transformation rules. In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to the works of Theophrastus and Eudemus for the first investigation of this kind of syllogisms. [1][2]
A type of ambiguity resulting from ambiguous grammatical structure, rather than the ambiguity of individual words. analethic logic A three-valued logic where the third truth value is the truth-value gap "neither true nor false" ("N"), and the designated values are "true" and "neither true nor false." [10] analysis 1.
Propositional calculus. Not to be confused with Propositional analysis. The propositional calculus[a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4][5] It deals with propositions [1] (which can be true or false) [6] and ...
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as ...