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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).	U+21D2 U+2192 U+2283	⇒ → ⊃	\Rightarrow \to \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	U+21D4 U+2261 U+2194	⇔ ≡ ↔	\Leftrightarrow \equiv \leftrightarrow
	if and only if; iff
	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)	U+00AC U+02DC	¬ ˜ ~	\lnot ˜\sim
	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.	U+2227 U+0026	&and; &amp;	\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.	U+2228	&or;	\lor
	or
	propositional logic
⊕ ⊻	exclusive disjunction	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.	U+2295 U+22BB	&oplus;	\oplus
	xor
	propositional logic, Boolean algebra
⊤ T 1	Tautology	The statement ⊤ is unconditionally true.	A ⇒ ⊤ is always true.	U+22A4	T	\top
	top
	propositional logic, Boolean algebra
⊥ F 0	Contradiction	The statement ⊥ is unconditionally false.	⊥ ⇒ A is always true.	U+22A5	&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.	U+2200	&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.	U+2203	&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.	U+2203 U+0021	&exist; !	\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+003A U+003D U+2261 U+003A U+229C	:= : &equiv; &hArr;	: = := \equiv \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.	U+0028 U+0029	( )	( )
	everywhere
⊢	inference	x ⊢ y means y is derived from x.	A → B ⊢ ¬B → ¬A	U+22A2		\vdash
	infers or is derived from
	propositional logic, first-order logic

Advanced and Rarely Used Logical symbols

These symbols are sorted by their Unicode value:

• U+00B7 ·: Center dot, an outdated way for denoting AND, still in use in electronics; for example "A·B" is the same as "A&B"
• ·: Center dot with a line above it (using HTML style). Outdated way for denoting NAND, for example "A·B" is the same as "A NAND B" or "A|B" or "¬(A & B)" See also Unicode "Dot operator" U+22C5

• U+0305 ̅ : overline, used as abbreviation for standard numerals. for example, using HTML style "4" is a shorthand for the standard numeral "SSSS0"
• ̅ : overline, an outdated way for denoting negation, still in use in electronics; for example "AVB" is the same as "¬(AVB)"
• ̅ : overline, a rarely used format for denoting Gödel numbers, for example "AVB" says the Gödel number of "(AVB)"

• U+2191 ↑ or U+007C | : Sheffer stroke, the sign for the NAND operator.
• U+2201 ∁: complement
• U+2204 ∄: strike out existential quantifier same as "¬∃"
• U+2234 ∴: therefore
• U+2235 ∵: because
• U+22A7 ⊧: is a model of
• U+22A8 ⊨: is true of
• U+22AC ⊬: strike out turnstile, the sign for "does not prove", for example T⊬P says "P is not a theorem of T"
• U+22AD ⊭: is not true of
• U+22BC ⊼: Another NAND operator, can also be rendered as ∧
• U+22BD ⊽: Another NOR operator, can also be rendered as V
• U+22C4 ◊: modal operator for "it is possible that", "it is not necessarily not" or rarely "it is not provable not" (in most modal logics it is defined as "¬◻¬")
• U+22C6 ⋆: Star operator, usually used for ad-hoc operators
• U+22A5 ⊥ or U+2193 ↓ : Webb-operator or Peirce arrow, the sign for NOR, confusingly, "⊥"is also the sign for contradiction or absurdity.

• U+2310 ⌐  : reversed not sign

• U+231C⌜ U+231D ⌝: corner quotes, also called "Quine quotes"; the standard symbol used for denoting Gödel number; for example "⌜G⌝" denotes the Gödel number of G. (Typographical note: although the quotes appears as a "pair" in unicode (231C and 231D), they are not symmetrical in some fonts. And in some fonts (for example Arial) they are only symmetrical in certain sizes. Alternatively the quotes can be rendered as ⌈⌉ and (unicode 2308 and 2309) or by using a negation symbol and a reversed negation symbol ⌐ ¬ in superscript mode. )

• U+25FB ◻ or U+25A1 □: modal operator for "it is necessary that" (in modal logic), or "it is provable that" (in provability logic), or "it is obligatory that" (in Deontic logic), or "It is believed that" (in Doxastic logic). Typographical note: there are many different "box" signs in unicode, some are NOT rendered as a box in non-western fonts. When using the modal operator in Web pages, it is important to specify the font.

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.

• U+27E1 ⟡:modal operator for never
• U+27E2 ⟢: modal operator for was never
• U+27E3 ⟣: modal operator for will never be
• U+27E4 ⟤: modal operator for was always
• U+27E5 ⟥: modal operator for will always be

• U+297D ⥽: right fishtail sign, sometimes used for "relation", also used for denoting various ad hoc relations (for example, for denoting "witnessing" in the context of Rosser's trick) See here for an image of glyph. Added to Unicode 3.2.0 .

See also

Logic portal

• Table of mathematical symbols
• Polish notation
• Logic Alphabet, a suggested set of logical symbols.
• Unicode Mathematical Operators

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.