List of logic symbols

In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols together with their name, pronunciation, and the related field of mathematics. Additionally, the third column contains an informal definition, the fourth column gives a short example, the fifth and sixth give the unicode location and name for use in HTML documents.[1] The last column provides the LaTeX symbol.

Outside logic, different symbols have the same meaning, and the same symbol can have different meanings, depending on the context.

Basic logic symbols

Name Explanation Examples Unicode
Read as

material implication AB is true only in the case that either A is false or B is true.

→ 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). U+21D2






implies; if .. then
propositional logic, Heyting algebra

material equivalence A B is true only if both A and B are false, or both A and B are true. x + 5 = y + 2    x + 3 = y U+21D4






if and only if; iff; means the same as
propositional logic


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)






\lnot or \neg
propositional logic


logical conjunction The 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. U+2227






\wedge or \land
propositional logic, Boolean algebra


logical (inclusive) disjunction The 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. U+2228





\lor or \vee
propositional logic, Boolean algebra

exclusive disjunction The statement AB is true when either A or B, but not both, are true. AB means the same. A) ⊕ A is always true, AA is always false. U+2295



propositional logic, Boolean algebra


Tautology The statement ⊤ is unconditionally true. A ⇒ ⊤ is always true. U+22A4


top, verum
propositional logic, Boolean algebra


Contradiction The statement ⊥ is unconditionally false. (The symbol ⊥ may also refer to perpendicular lines.) ⊥ ⇒ A is always true. U+22A5



bottom, falsum, falsity
propositional logic, Boolean algebra

universal quantification  x: P(x) or (x) P(x) means P(x) is true for all x.  n : n2 n. U+2200



for all; for any; for each
first-order logic
existential quantification  x: P(x) means there is at least one x such that P(x) is true.  n : n is even. U+2203 &#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 + 5 = 2n. U+2203 U+0021 &#8707; &#33; \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)
U+2254 (U+003A U+003D)


U+003A U+229C
&#8788; (&#58; &#61;)




is defined as
( )
precedence grouping Perform the operations inside the parentheses first. (8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1, but 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4. U+0028 U+0029 &#40; &#41; ( )
parentheses, brackets
Turnstile xy means y is provable from x (in some specified formal system). AB ⊢ ¬B → ¬A U+22A2 &#8866; \vdash
propositional logic, first-order logic
double turnstile xy means x semantically entails y AB ⊨ ¬B → ¬A U+22A8 &#8872; \vDash
propositional logic, first-order logic

Advanced and rarely used logical symbols

These symbols are sorted by their Unicode value:

Note that the following operators are rarely supported by natively installed fonts. If you wish to use these in a web page, you should always embed the necessary fonts so the page viewer can see the web page without having the necessary fonts installed in their computer.

Poland and Germany

As of 2014 in Poland, the universal quantifier is sometimes written and the existential quantifier as . The same applies for Germany.

See also


  1. "Named character references". HTML 5.1 Nightly. W3C. Retrieved 9 September 2015.
  2. Although this character is available in LaTeX, the MediaWiki TeX system doesn't support this character.
  3. Brody, Baruch A. (1973), Logic: theoretical and applied, Prentice-Hall, p. 93, ISBN 9780135401460, We turn now to the second of our connective symbols, the centered dot, which is called the conjunction sign.
  4. Quine, W.V. (1981): Mathematical Logic, §6
  5. Hintikka, Jaakko (1998), The Principles of Mathematics Revisited, Cambridge University Press, p. 113, ISBN 9780521624985.

Further reading

Józef Maria Bocheński (1959), A Précis of Mathematical Logic, trans., Otto Bird, from the French and German editions, Dordrecht, South Holland: D. Reidel.

External links

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