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In mathematics, proof by contrapositive, or proof by contraposition, is a rule of inference used in proofs, where one infers a conditional statement from its contrapositive. [15] In other words, the conclusion "if A, then B" is inferred by constructing a proof of the claim "if not B, then not A" instead. More often than not, this approach is ...
The superalternation is the contrapositive of the subalternation.) In these relations, the particular is the subaltern of the universal, which is the particular's superaltern. For example, if 'every man is white' is true, its contrary 'no man is white' is false. Therefore, the contradictory 'some man is white' is true.
In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form , the inverse refers to the sentence . Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to each other.
An immediate inference is an inference which can be made from only one statement or proposition. [1] For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" (Obverse). There are a number of immediate inferences which can validly be made using logical ...
There are two indefinite pronouns in Hindi: कोई koī (someone, somebody) and कुछ kuch (something). कुछ kuch is also used as an adjective (numeral and quantitative) and as an adverb meaning ‘some, a few, a little, partly.’. Similarly, कोई koī can be used as an adverb in the sense of ‘some, about.’.
Counterfactual conditional. Counterfactual conditionals (also contrafactual, subjunctive or X-marked) are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives, which are generally restricted ...
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 ...
There are many places to live in California other than San Diego. On the other hand, one can affirm with certainty that "if someone does not live in California" (non-Q), then "this person does not live in San Diego" (non-P). This is the contrapositive of the first statement, and it must be true if and only if the original statement is true ...