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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.
One valid argument form is known as modus ponens, not to be mistaken with modus tollens, which is another valid argument form that has a like-sounding name and structure. Modus ponens (sometimes abbreviated as MP) says that if one thing is true, then another will be. It then states that the first is true. The conclusion is that the second thing ...
Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [1][2][3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician.
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). [1] The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that ...
Antithesis (pl.: antitheses; Greek for "setting opposite", from ἀντι- "against" and θέσις "placing") is used in writing or speech either as a proposition that contrasts with or reverses some previously mentioned proposition, or when two opposites are introduced together for contrasting effect. [1][2] Antithesis can be defined as "a ...
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.
In propositional logic, modus ponens (/ ˈmoʊdəs ˈpoʊnɛnz /; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3] It can be summarized as " P implies Q. P is true. Therefore, Q must also be ...
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic, material implication[1][2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and ...