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In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
Therefore (Mathematical symbol for "therefore" is ), if it rains today, we will go on a canoe trip tomorrow". To make use of the rules of inference in the above table we let p {\displaystyle p} be the proposition "If it rains today", q {\displaystyle q} be "We will not go on a canoe today" and let r {\displaystyle r} be "We will go on a canoe ...
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
Therefore, not P. The first premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not the case. From these two premises it can be logically concluded that P, the antecedent of the conditional claim, is also not the case. For example:
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
A second example provides a first proposition that appears realistic and shows how an obviously flawed conclusion still arises under this fallacy. [3] To be on the cover of Vogue Magazine, one must be a celebrity or very beautiful. This month's cover was a celebrity. Therefore, this celebrity is not very beautiful.
For example, the physicist Albert Einstein's formula = is the quantitative representation in mathematical notation of mass–energy equivalence. [ 1 ] Mathematical notation was first introduced by François Viète at the end of the 16th century and largely expanded during the 17th and 18th centuries by René Descartes , Isaac Newton , Gottfried ...
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.