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Tautology It is a term that comes from a Greek word and refers to the repetition of oneself thought through different expressions . A tautology, for rhetoric, is a redundant statement .

It is common for tautologies to be considered as an error in the language or a lack of style. However, it is possible to appeal to tautologies to emphasize a certain idea. For example: prayer "I can confirm that the defendant is guilty since I saw the murder with my own eyes" presents an unnecessary clarification about the use of his eyes, since he could not have seen it by other means; Similarly, the emphasis of the word "own" can be omitted absolutely.

Other very common examples of tautology can be seen in the following sentences: "I will go upstairs to look for a book and come back", “I have to go outside to water the plants”. Whenever you climb it is up; Similarly, leaving means moving out of a place, so these clarifications lack sense and are unnecessary for understanding.

When tautology is a redundant explanation that does not provide new knowledge, we usually talk about truism or Truth of Perogrullo : "I am what I am". The expression in which redundant terms appear (such as "go up" or "to go outside"), on the other hand, is called pleonasm .

In the field of logic, a tautology is a formula of a system That is true for any interpretation. In other words, it is a logical expression that is true for all possible truth values ​​of its atomic components. To know if a given formula is a tautology, a truth table must be constructed.

True table

The table of true (also known as truth values ​​table) presents a compound proposition and its true value for each of the possible combinations that may occur with its elements. Its author was the American philosopher and scientist Charles Sanders Peirce, also known as the top representative of modern semiotics, and published it in the mid-1880s.

To configure a formal system, it is necessary to establish the definitions of each operator and the arguments must be presented in the form of logical-linguistic deductive reasoning, respond to a purely mathematical design and constitute an application logic Define your input and output variables.

The two possible values ​​that a truth table can throw are: true, which is expressed by the letter "V" or with the number "1" and indicates that the circuit is closed; false, represented by the letter "F" or the number "0", when a circuit is open. The propositions The variables to be analyzed are located at the top of the table, taking the place that is commonly used for field names.

The operators used in a real table are:

* denial: when running on a value indeed determined, throws the opposite (if originally it was true, returns false, and vice versa);

* conjunction: it is used to operate with two values ​​of truth, generally of two different propositions, and returns true when the two are, and false for the rest of the cases;

* disjunction: similar to the conjunction, but it is enough that one of the two propositions has true value to return such result;

* conditional: also known by the name of implication, take two propositions and throw false only when the first returns true and the second, false. For the remaining cases, the result is true;

* biconditional: operates on the truth values ​​of two propositions and returns true if both have the same value and false in the opposite case.

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