Table of logic symbols

Information about 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
	Should be read as
	Category
⇒ → ⊃	material implication	A ⇒ B 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	⇒ → ⊃	$\text{[math]}$ \Rightarrow $\text{[math]}$ \rightarrow $\text{[math]}$ \supset
	implies; if .. then
	propositional logic, Heyting algebra
⇔ ≡ ↔	material equivalence	A ⇔ B means A is true if B is true and A is false if B is false.	x + 5 = y +2 ⇔ x + 3 = y	8660 8596	⇔ &equiv; ↔	$\text{[math]}$ \Leftrightarrow $\text{[math]}$ \equiv $\text{[math]}$ \leftarrow
	if and only if; iff
	propositional logic
¬ ˜	logical negation	The 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	¬ &tilde; ~	$\text{[math]}$ \lnot \tilde{}
	not
	propositional logic
∧ &	logical conjunction	The statement A ∧ B 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; &	$\text{[math]}$ \land \&^[1]
	and
	propositional logic
∨	logical disjunction	The statement A ∨ B 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;	$\text{[math]}$ \lor
	or
	propositional logic
⊕ ⊻	exclusive or	The statement A ⊕ B is true when either A or B, but not both, are true. A ⊻ B means the same.	(¬A) ⊕ A is always true, A ⊕ A is always false.	8853 8891	&oplus;	$\text{[math]}$ \oplus
	xor
	propositional logic, Boolean algebra
⊤ T 1	logical truth	The statement ⊤ is unconditionally true.	A ⇒ ⊤ is always true.	8868	T	$\text{[math]}$ \top
	top
	propositional logic, Boolean algebra
⊥ F 0	logical falsity	The statement ⊥ is unconditionally false.	⊥ ⇒ A is always true.	8869	&perp; F	$\text{[math]}$ \bot
	bottom
	propositional logic, Boolean algebra
∀	universal quantification	∀ x: P(x) means P(x) is true for all x.	∀ n ∈ N: n² ≥ n.	8704	∀	$\text{[math]}$ \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	∃	$\text{[math]}$ \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	∃ !	$\text{[math]}$ \exists !
	there exists exactly one
	first-order logic
:= ≡ :⇔	definition	x := 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; ⇔	$\text{[math]}$ := $\text{[math]}$ \equiv $\text{[math]}$ \Leftrightarrow
	is defined as
	everywhere
( )	precedence grouping	Perform the operations inside the parentheses first.	(8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.	40 41	( )	$\text{[math]}$ ( )

	everywhere
⊢	inference	x ⊢ y means y is derived from x.	A → B ⊢ ¬B → ¬A	8866		$\text{[math]}$ \vdash
	infers or is derived from
	propositional logic, first-order logic

Special characters

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Notes

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

External links

Named character entities in HTML 4.0.

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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.
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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.
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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.
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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").
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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.
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(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.
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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
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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.
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“Iff” redirects here. For other uses, see IFF.

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
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For other uses, see .

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.
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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
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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).
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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.
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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.
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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.
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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.
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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.
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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,
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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.
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