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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.
Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. [1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion.
A function that takes two arguments. In logic and mathematics, this is often a function that combines two values to produce a third value, such as addition or multiplication in arithmetic. binary relation A relation involving two terms or elements, defining a particular relationship between pairs of objects from two sets (or from one set to ...
Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. As a formal science , logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of ...
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.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .
Logic is interested in whether arguments are correct, i.e. whether their premises support the conclusion. [7] These general characterizations apply to logic in the widest sense, i.e., to both formal and informal logic since they are both concerned with assessing the correctness of arguments. [ 8 ]
A logical argument, seen as an ordered set of sentences, has a logical form that derives from the form of its constituent sentences; the logical form of an argument is sometimes called argument form. [6] Some authors only define logical form with respect to whole arguments, as the schemata or inferential structure of the argument. [7]