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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 .
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
An area of algebra in which the values of the variables are the truth values true and false, typically used in computer science, logic, and mathematical logic. Boolean negation A form of negation where the negation of a non-true proposition is true, and the negation of a non-false proposition is false. [34] [35] [36] Boolean operator
Wedge (∧) is a symbol that looks similar to an in-line caret (^). It is used to represent various operations. In Unicode, the symbol is encoded U+2227 ∧ LOGICAL AND (∧, ∧) and by \wedge and \land in TeX. The opposite symbol (∨) is called a vel, or sometimes a (descending) wedge.
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...
When drawing a logic symbol, one passes through each square with assigned F values while stopping in a square with assigned T values. In the extreme examples, the symbol for tautology is a X (stops in all four squares), while the symbol for contradiction is an O (passing through all squares without stopping). The square matrix corresponding to ...
Forcing (mathematics) Boolean-valued model; Kripke semantics. General frame; Predicate logic. First-order logic. Infinitary logic; Many-sorted logic; Higher-order logic. Lindström quantifier; Second-order logic; Soundness theorem; Gödel's completeness theorem. Original proof of Gödel's completeness theorem; Compactness theorem; Löwenheim ...
In formal languages, truth functions are represented by unambiguous symbols.This allows logical statements to not be understood in an ambiguous way. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives.