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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.
Proof by contraposition infers the statement "if p then q" by establishing the logically equivalent contrapositive statement: "if not q then not p". For example, contraposition can be used to establish that, given an integer , if is even, then is even: Suppose is not even.
Expository writing is a type of writing where the purpose is to explain or inform the audience about a topic. [13] It is considered one of the four most common rhetorical modes. [14] The purpose of expository writing is to explain and analyze information by presenting an idea, relevant evidence, and appropriate discussion.
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical argument, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
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.
For example, the phrase, "John, my best friend" uses the scheme known as apposition. Tropes (from Greek trepein, 'to turn') change the general meaning of words. An example of a trope is irony, which is the use of words to convey the opposite of their usual meaning ("For Brutus is an honorable man; / So are they all, all honorable men").
The author uses narrative and stylistic devices to create the sense of an unedited interior monologue, characterized by leaps in syntax and punctuation that trace a character's fragmentary thoughts and sensory feelings. The outcome is a highly lucid perspective with a plot. Not to be confused with free writing. An example is Ulysses. At one ...
The example above is fortunate in that there is a procedure to generate all the conjuncts. However, if an assertion were to be made about every irrational number, there would be no way to enumerate all the conjuncts, since irrationals cannot be enumerated. A succinct, equivalent formulation which avoids these problems uses universal quantification: