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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.
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.
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.
The essay is to consist of an introduction three or more sentences long and containing a thesis statement, a conclusion incorporating all the writer's commentary and bringing the essay to a close, and two or three body paragraphs; Schaffer herself preferred to teach a four-paragraph essay rather than the traditional five-paragraph essay.
The writing of an expository essay often consists of the following steps: organizing thoughts (brainstorming), researching a topic, developing a thesis statement, writing the introduction, writing the body of essay, and writing the conclusion. [14]
Each proposition has three essential parts: a subject, a predicate, and a copula connecting the subject to the predicate. [107] For example, the proposition "Socrates is wise" is made up of the subject "Socrates", the predicate "wise", and the copula "is". [108] The subject and the predicate are the terms of the proposition. Aristotelian logic ...
1 Discussion on merging contrapositive and contraposition. 4 comments. 2 Contraposition vs transposition. 2 comments. 3 This article needs rewriting. 6 comments. 4 ...
For example, consider the true statement "If I am a human, then I am mortal." The converse of that statement is "If I am mortal, then I am a human," which is not necessarily true. However, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition.