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In propositional logic, tautology is either of two commonly used rules of replacement. [1] [2] [3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are: The principle of idempotency of disjunction:
Many logicians in the early 20th century used the term 'tautology' for any formula that is universally valid, whether a formula of propositional logic or of predicate logic. In this broad sense, a tautology is a formula that is true under all interpretations, or that is logically equivalent to the negation of a contradiction.
A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
'''bold''' ''italics'' <sup>superscript</sup> <sub>superscript</sub> → bold: → italics: → superscript → subscript <s>strikeout</s> <u>underline</u> <big>big ...
Wiki markup quick reference (PDF download) For a full list of editing commands, see Help:Wikitext; For including parser functions, variables and behavior switches, see Help:Magic words; For a guide to displaying mathematical equations and formulas, see Help:Displaying a formula; For a guide to editing, see Wikipedia:Contributing to Wikipedia
This cheat sheet is the aftermath of hours upon hours of research on all of the teams in this year’s tournament field. I’ve listed each teams’ win and loss record, their against the spread totals, and their record in the last ten games. Also included are the three leading high scorers along with
Transformation rules; Propositional calculus; Rules of inference; Implication introduction / elimination (modus ponens) Biconditional introduction / elimination; Conjunction introduction / elimination; Disjunction introduction / elimination; Disjunctive / hypothetical syllogism; Constructive / destructive dilemma
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