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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.
The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent. If monkeys are purple, then fish speak Klingon. "Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple".
The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences: (2) The relation is a priori, i.e., it can be determined with or without regard to empirical evidence (sense experience); and (3) The logical consequence ...
If separating words using spaces is also permitted, the total number of known possible meanings rises to 58. [38] Czech has the syllabic consonants [r] and [l], which can stand in for vowels. A well-known example of a sentence that does not contain a vowel is Strč prst skrz krk, meaning "stick your finger through the neck."
Stormont opposition leader Matthew O’Toole said there is ‘a crisis of accountability in our politics’.
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
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