Inlogic, a set ofsymbols 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 ofmathematics. Additionally, the subsequent columns contains an informal explanation, a short example, theUnicode location, the name for use inHTML documents,^[1] and theLaTeX symbol.

Symbol	Unicode value (hexadecimal)	HTML codes	LaTeX symbol	Logic Name	Read as	Category	Explanation	Examples
⇒ → ⊃	U+21D2 U+2192 U+2283	⇒ → ⊃ ⇒ → ⊃	${\displaystyle \Rightarrow }$\Rightarrow ${\displaystyle ⟹}$\implies ${\displaystyle \to }$\to or \rightarrow ${\displaystyle \supset }$\supset	material conditional (material implication)	implies, if P then Q, it is not the case that P and not Q	propositional logic,Boolean algebra, Heyting algebra	${\displaystyle A\Rightarrow B}$ is false whenA is true andB is false but true otherwise. In other mathematical contexts, seeglossary of mathematical symbols,${\displaystyle \to }$ may indicate the domain and codomain of afunction and${\displaystyle \supset }$ may meansuperset.	${\displaystyle x=2\Rightarrow x^2=4}$ is true, but${\displaystyle x^2=4\Rightarrow x=2}$ is in general false (sincex could be −2).
⇔ ↔ ≡	U+21D4 U+2194 U+2261	⇔ ↔ ≡ ⇔ ↔ ≡	${\displaystyle \iff }$\Leftrightarrow ${\displaystyle ⟺}$\iff ${\displaystyle \leftrightarrow }$\leftrightarrow ${\displaystyle \equiv }$\equiv	material biconditional (material equivalence)	if and only if, iff, xnor	propositional logic,Boolean algebra	${\displaystyle A\iff B}$ is true only if both A and B are false, or bothA and B are true. Whether a symbol means amaterial biconditional or alogical equivalence, depends on the author’s style.	${\displaystyle x+5=y+2\iff x+3=y}$
¬ ~ ! ′	U+00AC U+007E U+0021 U+2032	¬ ˜ ! ′ ¬ ˜ ! ′	${\displaystyle \mathrm{\neg }}$\lnot or \neg ${\displaystyle \sim }$\sim ${\displaystyle {}^{\prime }}$ '	negation	not	propositional logic,Boolean algebra	The statement${\displaystyle \mathrm{\neg }A}$ is true if and only ifA is false. A slash placed through another operator is the same as${\displaystyle \mathrm{\neg }}$ placed in front. The prime symbol is placed after the negated thing, e.g.${\displaystyle p^{\prime }}$[2]	${\displaystyle \mathrm{\neg }(\mathrm{\neg }A)\iff A}$ ${\displaystyle x\ne y\iff \mathrm{\neg }(x=y)}$
∧ · &	U+2227 U+00B7 U+0026	&#8743; &#183; &#38; &and; &middot; &amp;	${\displaystyle \wedge }$\wedge or \land ${\displaystyle \cdot }$\cdot \&[3]	logical conjunction	and	propositional logic,Boolean algebra	The statementA ∧ B is true ifA and B are both true; otherwise, it is false.	n < 4  ∧ n >2  ⇔ n = 3 whenn is anatural number.
∨ + ∥	U+2228 U+002B U+2225	&#8744; &#43; &#8741; &or; &plus; &parallel;	${\displaystyle \vee }$\lor or \vee ${\displaystyle \parallel }$\parallel	logical (inclusive) disjunction	or	propositional logic,Boolean algebra	The statementA ∨ B is true ifA orB (or both) are true; if both are false, the statement is false.	n ≥ 4  ∨ n ≤ 2  ⇔n ≠ 3 whenn is anatural number.
⊕ ⊻ ↮ ≢	U+2295 U+22BB U+21AE U+2262	&#8853; &#8891; &#8622; &#8802; &oplus; &veebar; — &nequiv;	${\displaystyle \oplus }$\oplus ${\displaystyle ⊻}$\veebar ${\displaystyle \not\equiv }$\not\equiv	exclusive disjunction	xor, either ... or ... (but not both)	propositional logic,Boolean algebra	The statement${\displaystyle A\oplus B}$ is true when eitherA orB, but not both, are true. This is equivalent to ¬(A ↔B), hence the symbols${\displaystyle \nleftrightarrow }$ and${\displaystyle \not\equiv }$.	${\displaystyle \mathrm{\neg }A\oplus A}$ is always true and${\displaystyle A\oplus A}$ is always false (ifvacuous truth is excluded).
⊤ T 1	U+22A4	&#8868; &top;	${\displaystyle \mathrm{\top }}$\top	true (tautology)	top, truth, tautology, verum, full clause	propositional logic,Boolean algebra,first-order logic	${\displaystyle \mathrm{\top }}$ denotes a proposition that is always true.	The proposition${\displaystyle \mathrm{\top }\vee P}$ is always true since at least one of the two is unconditionally true.
⊥ F 0	U+22A5	&#8869; &perp;	${\displaystyle \mathrm{\perp }}$\bot	false (contradiction)	bottom, falsity, contradiction, falsum, empty clause	propositional logic,Boolean algebra,first-order logic	${\displaystyle \mathrm{\perp }}$ denotes a proposition that is always false. The symbol ⊥ may also refer toperpendicular lines.	The proposition${\displaystyle \mathrm{\perp }\wedge P}$ is always false since at least one of the two is unconditionally false.
∀ ()	U+2200	&#8704; &forall;	${\displaystyle \mathrm{\forall }}$\forall	universal quantification	given any, for all, for every, for each, for any	first-order logic	${\displaystyle \mathrm{\forall }x}$ ${\displaystyle P(x)}$ or ${\displaystyle (x)}$ ${\displaystyle P(x)}$ says “given any${\displaystyle x}$,${\displaystyle x}$ has property${\displaystyle P}$.”	${\displaystyle \mathrm{\forall }n\in \mathbb{N}:n^2\ge n.}$
∃	U+2203	&#8707; &exist;	${\displaystyle \mathrm{\exists }}$\exists	existential quantification	there exists, for some	first-order logic	${\displaystyle \mathrm{\exists }x}$ ${\displaystyle P(x)}$ says “there exists an${\displaystyle x}$ (at least one) such that${\displaystyle x}$ has property${\displaystyle P}$.”	${\displaystyle \mathrm{\exists }n\in \mathbb{N}:}$n is even.
∃!	U+2203 U+0021	&#8707; &#33; &exist;!	${\displaystyle \mathrm{\exists }!}$\exists !	uniqueness quantification	there existsexactly one	first-order logic (abbreviation)	${\displaystyle \mathrm{\exists }!x}$${\displaystyle P(x)}$ says “there exists exactly one${\displaystyle x}$ such that${\displaystyle x}$ has property${\displaystyle P}$.” Only${\displaystyle \mathrm{\forall }}$ and${\displaystyle \mathrm{\exists }}$ are part of formal logic. ${\displaystyle \mathrm{\exists }!x}$${\displaystyle P(x)}$ is an abbreviation for ${\displaystyle \mathrm{\exists }x\mathrm{\forall }y(P(y)\leftrightarrow y=x)}$	${\displaystyle \mathrm{\exists }!n\in \mathbb{N}:n+5=2n.}$
( )	U+0028 U+0029	&#40; &#41; &lpar; &rpar;	${\displaystyle ()}$ ( )	precedence grouping	parentheses; brackets	almost all logic syntaxes, as well as metalanguage	Perform the operations inside the parentheses first.	(8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1, but8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4.
${\displaystyle \mathbb{D}}$	U+1D53B	&#120123; &Dopf;	\mathbb{D}	domain of discourse	domain of discourse	metalanguage (first-order logic semantics)		${\displaystyle \mathbb{D}\mathbb{:}\mathbb{R}}$
⊢	U+22A2	&#8866; &vdash;	${\displaystyle ⊢}$\vdash	syntactic consequence	proves, syntactically entails (single) turnstile	metalanguage (metalogic)	${\displaystyle A⊢B}$ says “${\displaystyle B}$ is a theorem of${\displaystyle A}$”. In other words, ${\displaystyle A}$ proves${\displaystyle B}$ via a deductive system.	${\displaystyle (A\to B)⊢(\mathrm{\neg }B\to \mathrm{\neg }A)}$ (eg. by usingnatural deduction)
⊨	U+22A8	&#8872; &vDash;	${\displaystyle \models }$\vDash, \models	semantic consequence orsatisfaction	(semantically) entails or satisfies, modelsdouble turnstile	metalanguage (metalogic)	${\displaystyle A\models B}$ says “in everymodel, it is not the case that${\displaystyle A}$ is true and${\displaystyle B}$ is false”. ${\displaystyle \mathcal{M},\sigma \models B}$ says a formula ${\displaystyle B}$ is true in a model${\displaystyle \mathcal{M}}$ with variable assignment${\displaystyle \sigma }$.	${\displaystyle (A\to B)\models (\mathrm{\neg }B\to \mathrm{\neg }A)}$ (eg. by usingtruth tables)
≡ ⟚ ⇔	U+2261 U+27DA U+21D4	&#8801; — &#8660;&equiv;—&hArr;	${\displaystyle \equiv }$\equiv ${\displaystyle \iff }$\Leftrightarrow	logical equivalence	is logically equivalent to	metalanguage (metalogic)	It’s when${\displaystyle A\models B}$ and${\displaystyle B\models A}$. Whether a symbol means amaterial biconditional or alogical equivalence, depends on the author’s style.	${\displaystyle (A\to B)\equiv (\mathrm{\neg }A\vee B)}$
⊬	U+22AC		⊬\nvdash		does not syntactically entail (does not prove)	metalanguage (metalogic)	${\displaystyle A⊬B}$ says “${\displaystyle B}$ is not a theorem of${\displaystyle A}$”. In other words, ${\displaystyle B}$ is not derivable from${\displaystyle A}$ via a deductive system.	${\displaystyle A\vee B⊬A\wedge B}$
⊭	U+22AD		⊭\nvDash		does not semantically entail	metalanguage (metalogic)	${\displaystyle A⊭B}$ says “${\displaystyle A}$ does not guarantee the truth of${\displaystyle B}$ ”. In other words, ${\displaystyle A}$ does not make${\displaystyle B}$ true.	${\displaystyle A\vee B⊭A\wedge B}$
□	U+25A1		${\displaystyle ◻}$\Box	necessity (in a model)	box; it is necessary that	modal logic	modal operator for “it is necessary that” inalethic logic, “it is provable that” inprovability logic, “it is obligatory that” indeontic logic, “it is believed that” indoxastic logic.	${\displaystyle ◻\mathrm{\forall }xP(x)}$ says “it is necessary that everything has property${\displaystyle P}$”
◇	U+25C7		${\displaystyle ◊}$\Diamond	possibility (in a model)	diamond; it is possible that	modal logic	modal operator for “it is possible that”, (in most modal logics it is defined as “¬□¬”, “it is not necessarily not”).	${\displaystyle ◊\mathrm{\exists }xP(x)}$ says “it is possible that something has property${\displaystyle P}$”
∴	U+2234		∴\therefore	therefore	therefore	metalanguage	abbreviation for “therefore”.
∵	U+2235		∵\because	because	because	metalanguage	abbreviation for “because”.
≔ ≜ ≝	U+2254 U+225C U+225D	&#8788; &coloneq;	≔ \coloneqq ${\displaystyle :=}$:= ${\displaystyle \triangleq }$\triangleq ${\displaystyle \stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}}$ \stackrel{ \scriptscriptstyle \mathrm{def}}{=}	definition	is defined as	metalanguage	${\displaystyle a:=b}$ means "from now on,${\displaystyle a}$ is defined to be another name for${\displaystyle b}$." This is a statement in the metalanguage, not the object language. The notation${\displaystyle a\equiv b}$ may occasionally be seen in physics, meaning the same as${\displaystyle a:=b}$.	${\displaystyle \cosh x:=\frac{e^x+e^{-x}}{2}}$
↑ | ⊼	U+2191 U+007C U+22BC		${\displaystyle \uparrow }$ \uparrow	Sheffer stroke, NAND	NAND, not both up arrow	Propositional logic	NAND is the negation of conjunction so${\displaystyle A\uparrow B}$ is true if and only if it's not the case that bothA and B are true. See alsoNAND gate
↓ ⊽	U+2193 U+22BC		${\displaystyle \downarrow }$ \downarrow	Peirce Arrow, NOR	nor down arrow	Propositional logic	NOR is the negation of conjunction so${\displaystyle A\downarrow B}$ is true if and only if bothA and B are false. See alsoNOR gate

The following symbols are either advanced and context-sensitive or very rarely used:

Symbol	Unicode value (hexadecimal)	HTML value (decimal)	HTML entity (named)	LaTeX symbol	Logic Name	Read as	Category	Explanation
⥽	U+297D			\strictif	right fish tail			Sometimes used for “relation”, also used for denoting various ad hoc relations (for example, for denoting “witnessing” in the context ofRosser's trick). The fish tail is also used as strict implication by C.I.Lewis${\displaystyle p}$ ⥽${\displaystyle q\equiv ◻(p\to q)}$.
̅	U+0305				combining overline			Used format for denotingGödel numbers. Using HTML style “4̅” is an abbreviation for the standard numeral “SSSS0”. It may also denote a negation (used primarily in electronics).
⌜ ⌝	U+231C U+231D			\ulcorner \urcorner	top left corner top right corner			Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions;[4] also used for denotingGödel number;[5] 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. In some fonts (for example Arial) they are only symmetrical in certain sizes. Alternatively the quotes can be rendered as ⌈ and ⌉ (U+2308 and U+2309) or by using a negation symbol and a reversed negation symbol ⌐ ¬ in superscript mode.)
∄	U+2204			\nexists	there does not exist			Strike out existential quantifier. “¬∃” used some times instead.
⊙	U+2299			\odot	circled dot operator			A sign for the XNOR operator (material biconditional and XNOR are the same operation).
⟛	U+27DB				left and right tack			“Proves and is proved by”.
⊩	U+22A9				forces			One of this symbol’s uses is to mean “truthmakes” in the truthmaker theory of truth. It is also used to mean “forces” in the set theory method of forcing.
⟡	U+27E1				white concave-sided diamond	never	modal operator
⟢	U+27E2				white concave-sided diamond with leftwards tick	was never	modal operator
⟣	U+27E3				white concave-sided diamond with rightwards tick	will never be	modal operator
⟤	U+25A4				white square with leftwards tick	was always	modal operator
⟥	U+25A5				white square with rightwards tick	will always be	modal operator
⋆	U+22C6				star operator			May sometimes be used for ad-hoc operators.
⌐	U+2310				reversed not sign
⨇	U+2A07				two logical AND operator

• Glossary of logic
• Józef Maria Bocheński
• List of notation used in Principia Mathematica
• List of mathematical symbols
• Logic alphabet, a suggested set of logical symbols
• Logic gate § Symbols
• Logical connective
• Mathematical operators and symbols in Unicode
• Non-logical symbol
• Polish notation
• Truth function
• Truth table
• Wikipedia:WikiProject Logic/Standards for notation

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

• Named character entities inHTML 4.0

• Mathematical notation
• Logic symbols

• Articles with short description
• Short description is different from Wikidata