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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.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Q.E.D. or QED is an initialism of the Latin phrase quod erat demonstrandum, meaning "that which was to be demonstrated".Literally, it states "what was to be shown". [1] ...
In English the words therefore, so, because and hence typically separate the premises from the conclusion of an argument. Thus: Socrates is a man, all men are mortal therefore Socrates is mortal is an argument because the assertion Socrates is mortal follows from the preceding statements.
Thus in intuitionistic logic proof by contradiction is not universally valid, but can only be applied to the ¬¬-stable propositions. An instance of such a proposition is a decidable one, i.e., satisfying P ∨ ¬ P {\displaystyle P\lor \lnot P} .
A conjunctive adverb, adverbial conjunction, or subordinating adverb is an adverb that connects two clauses by converting the clause it introduces into an adverbial modifier of the verb in the main clause.
Therefore, the simple conclusion above may be false. Example 5 Since the 1950s, both the atmospheric CO 2 level and obesity levels have increased sharply. Hence, atmospheric CO 2 causes obesity. Richer populations tend to eat more food and produce more CO 2. Example 6 HDL ("good") cholesterol is negatively correlated with incidence of heart attack.
The form of a modus tollens argument is a mixed hypothetical syllogism, with two premises and a conclusion: . If P, then Q. Not Q. Therefore, not P.. The first premise is a conditional ("if-then") claim, such as P implies Q.