# Table of logic symbols

In logic, a set of symbols is commonly used to express logical representation. As logicians are familiar with these symbols, they are not explained each time they are used. So, for students of logic, the following table lists many common symbols together with their name, pronunciation and related field of mathematics. Additionally, the third column contains an informal definition, and the fourth column gives a short example.

Be aware that, outside of logic, different symbols have the same meaning, and the same symbol has, depending on the context, different meanings.

## Basic logic symbols

Symbol
Name Explanation Examples Unicode
Value
HTML
Entity
LaTex
symbol
Category

material implicationAB means if A is true then B is also true; if A is false then nothing is said about B.

→ may mean the same as ⇒ (the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols).

⊃ may mean the same as ⇒ (the symbol may also mean superset).
x = 2  ⇒  x2 = 4 is true, but x2 = 4   ⇒  x = 2 is in general false (since x could be −2).8658

8594

8835
&rArr;
&rarr;
&sup;
\Rightarrow
\rightarrow
\supset
implies; if .. then
propositional logic, Heyting algebra

material equivalenceA ⇔ B means A is true if B is true and A is false if B is false.x + 5 = y +2  ⇔  x + 3 = y8660

8596
&hArr;
&equiv;
&harr;
\Leftrightarrow
\equiv
\leftarrow
if and only if; iff
propositional logic
¬

˜
logical negationThe statement ¬A is true if and only if A is false.

A slash placed through another operator is the same as "¬" placed in front.
¬(¬A) ⇔ A
x ≠ y  ⇔  ¬(x =  y)
172

732
&not;
&tilde;
~
\lnot
\tilde{}
not
propositional logic

&
logical conjunctionThe statement AB is true if A and B are both true; else it is false.n < 4  ∧  n >2  ⇔  n = 3 when n is a natural number.8743

38
&and;
&
\land
\&[1]
and
propositional logic
logical disjunctionThe statement AB is true if A or B (or both) are true; if both are false, the statement is false.n ≥ 4  ∨  n ≤ 2  ⇔ n ≠ 3 when n is a natural number.8744 &or; \lor
or
propositional logic

exclusive orThe statement AB is true when either A or B, but not both, are true. A B means the same.A) ⊕ A is always true, AA is always false.8853

8891
&oplus; \oplus
xor
propositional logic, Boolean algebra

T

1
logical truthThe statement ⊤ is unconditionally true.A ⇒ ⊤ is always true.8868 T \top
top
propositional logic, Boolean algebra

F

0
logical falsityThe statement ⊥ is unconditionally false.⊥ ⇒ A is always true.8869 &perp;
F
\bot
bottom
propositional logic, Boolean algebra
universal quantification∀ x: P(x) means P(x) is true for all x.∀ n ∈ N: n2 ≥ n.8704 &forall; \forall
for all; for any; for each
predicate logic
existential quantification∃ x: P(x) means there is at least one x such that P(x) is true.∃ n ∈ N: n is even.8707 &exist; \exists
there exists
first-order logic
∃!
uniqueness quantification∃! x: P(x) means there is exactly one x such that P(x) is true.∃! n ∈ N: n + 5 = 2n.8707 33 &exist; ! \exists !
there exists exactly one
first-order logic
:=

:⇔
definitionx := y or x ≡ y means x is defined to be another name for y (but note that ≡ can also mean other things, such as congruence).

P :⇔ Q means P is defined to be logically equivalent to Q.
cosh x := (1/2)(exp x + exp (−x))

A XOR B :⇔ (A ∨ B) ∧ ¬(A ∧ B)
58 61

8801

58 8660
:=
: &equiv;
&hArr;
:=
\equiv
\Leftrightarrow
is defined as
everywhere
( )
precedence groupingPerform the operations inside the parentheses first.(8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.40 41 ( ) ( )
everywhere
inferencex y means y is derived from x.AB ¬B → ¬A8866 \vdash
infers or is derived from
propositional logic, first-order logic

## Special characters

Technical note: Due to technical limitations, some browsers may not display the special characters in this article. Some characters may be rendered as boxes, question marks, or other symbols, depending on your browser, operating system, and installed fonts. Even if you have ensured that your browser is interpreting the article as UTF-8 encoded and you have installed a font that supports a wide range of Unicode, such as Code2000, Arial Unicode MS, Lucida Sans Unicode or one of the free software Unicode fonts, you may still need to use a different browser, as browser capabilities vary in this regard.

## Notes

1. ^ Although this character is available in LaTex, the Mediawiki TeX system doesn't support this character.

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.
Latex refers generically to a stable dispersion (emulsion) of polymer microparticles in an aqueous medium. Latexes may be natural or synthetic. Latex as found in nature is the milky sap of many plants that coagulates on exposure to air.
The material conditional, also known as the material implication or truth functional conditional, expresses a property of certain conditionals in logic. In propositional logic, it expresses a binary truth function ⊃ from truth-values to truth-values.
function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output").
u × v means the cross product of vectors u and v (1,2,5) × (3,4,−1) =
(−22, 16, − 2)
cross

·
multiplication 3 · 4 means the multiplication of 3 by 4.
(See also Subset for the uncapitalized use of the word "superset" in mathematics.)

SuperSet Software was a group founded by friends and former Eyring Research Institute (ERI) co-workers Drew Major, Dale Neibaur, Kyle Powell and later joined by Mark Hurst.
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules
In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras. Heyting algebras arise as models of intuitionistic logic, a logic in which the law of excluded middle does not in general hold.
If and only if, in logic and fields that rely on it such as mathematics and philosophy, is a logical connective between statements which means that the truth of either one of the statements
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules

In logic and mathematics, negation or not is an operation on logical values, for example, the logical value of a proposition, that sends true to false and false to true.
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules
In logic and/or mathematics, logical conjunction or and is a two-place logical operation that results in a value of true if both of its operands are true, otherwise a value of false!

## Definition

Logical conjunction
In mathematics, a natural number can mean either an element of the set (i.e the positive integers or the counting numbers) or an element of the set (i.e. the non-negative integers).
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules
or, also known as logical disjunction or inclusive disjunction is a logical operator that results in true whenever one or more of its operands are true. In grammar, or is a coordinating conjunction.
In mathematics, a natural number can mean either an element of the set (i.e the positive integers or the counting numbers) or an element of the set (i.e. the non-negative integers).
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules
exclusive disjunction, also called exclusive or, (symbolized XOR or EOR), is a type of logical disjunction on two operands that results in a value of "true" if and only if exactly one of the operands has a value of "true.
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules

In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules

In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules

In predicate logic, universal quantification is an attempt to formalize the notion that something (a logical predicate) is true for everything, or every relevant thing.
predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified.
In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. The logical operator symbol ∃ called the existential quantifier is used to denote existential quantification.
First-order logic (FOL) is a formal deductive system used by mathematicians, philosophers, linguists, and computer scientists. It goes by many names, including: first-order predicate calculus (FOPC), the lower predicate calculus,
one and only one" is used to indicate that exactly one object with a certain property exists. In mathematical logic, this sort of quantification is known as uniqueness quantification or unique existential quantification.