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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.
The symbol is used to denote negation. For example, if P(x) is the predicate "x is greater than 0 and less than 1", then, for a domain of discourse X of all natural numbers, the existential quantification "There exists a natural number x which is greater than 0 and less than 1" can be symbolically stated as:
U+003C < LESS-THAN SIGN: Less than or equal A≤B: Comparison: 1 if true, 0 if false U+2264 ≤ LESS-THAN OR EQUAL TO: Equal: A=B: Comparison: 1 if true, 0 if false U+003D = EQUALS SIGN: Greater than or equal A≥B: Comparison: 1 if true, 0 if false U+2265 ≥ GREATER-THAN OR EQUAL TO: Greater than A>B: Comparison: 1 if true, 0 if false U+003E ...
A predicate symbol (or relation symbol) with some valence (or arity, number of arguments) greater than or equal to 0. These are often denoted by uppercase letters such as P, Q and R. Examples: In P(x), P is a predicate symbol of valence 1. One possible interpretation is "x is a man".
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 and is sometimes expressed as , ::, , or , depending on the notation being used.
In languages such as C, relational operators return the integers 0 or 1, where 0 stands for false and any non-zero value stands for true. An expression created using a relational operator forms what is termed a relational expression or a condition. Relational operators can be seen as special cases of logical predicates.
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 ...
However, when exponentiation is represented by an explicit symbol such as a caret (^) or arrow (↑), there is no common standard. For example, Microsoft Excel and computation programming language MATLAB evaluate a^b^c as (a b) c, but Google Search and Wolfram Alpha as a (b c). Thus 4^3^2 is evaluated to 4,096 in the first case and to 262,144 ...