List of logic symbols#

https://en.wikipedia.org/wiki/List_of_logic_symbols
한글 https://ko.wikipedia.org/wiki/%EC%88%98%ED%95%99_%EA%B8%B0%ED%98%B8
In logic, a set of symbols 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 of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents,[1] and the LaTeX symbol.

Symbol	Unicode value (hexadecimal)	HTML codes	LaTeX symbol	Logic Name	Read as	Category	Explanation	Examples
⇒ → ⊃	U+21D2 U+2192 U+2283	⇒ → ⊃ ⇒ → ⊃	$\Rightarrow$ \Rightarrow $\implies$ \implies $\to$ \to or \rightarrow $\supset$ \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	$A\Rightarrow B$ is false when $A$ is true and $B$ is false but true otherwise. In other mathematical contexts, see glossary of mathematical symbols, $\rightarrow$ may indicate the domain and codomain of a function and $\supset$ may mean superset.	$x=2\Rightarrow x^{2}=4$ is true, but $x^{2}=4\Rightarrow x=2$ is in general false (since $x$ could be −2).
⇔ ↔ ≡	U+21D4 U+2194 U+2261	⇔ ↔ ≡ ⇔ &LeftRightArrow; &equiv;	$\Leftrightarrow$ \Leftrightarrow $\iff$ \iff $\leftrightarrow$ \leftrightarrow $\equiv$ \equiv	material biconditional (material equivalence)	if and only if, iff, xnor	propositional logic, Boolean algebra	$A\Leftrightarrow B$ is true only if both $A$ and $B$ are false, or both $A$ and $B$ are true. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.	$x+5=y+2\Leftrightarrow x+3=y$
¬ ~ ! ′	U+00AC U+007E U+0021 U+2032	¬ ˜ ! ′ ¬ &tilde; &excl; ′	$\neg$ \lnot or \neg $\sim$ \sim $'$ '	negation	not	propositional logic, Boolean algebra	The statement $\lnot A$ is true if and only if $A$ is false. A slash placed through another operator is the same as $\neg$ placed in front. The prime symbol is placed after the negated thing, e.g. $p'$ ^[2]	$\neg (\neg A)\Leftrightarrow A$ $x\neq y\Leftrightarrow \neg (x=y)$
∧ · &	U+2227 U+00B7 U+0026	∧ · & &and; · &	$\wedge$ \wedge or \land $\cdot$ \cdot $\&$ \&^[3]	logical conjunction	and	propositional logic, Boolean algebra	The statement A ∧ B is true if A and B are both true; otherwise, it is false.	$n < 4 \land$ $n >2 \Leftrightarrow$ $n = 3$ when n is a natural number.
∨ + ∥	U+2228 U+002B U+2225	∨ + ∥ &or; + &parallel;	$\lor$ \lor or \vee $\parallel$ \parallel	logical (inclusive) disjunction	or	propositional logic, Boolean algebra	The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false.	$n \geq 4 \lor n \leq 2 \Leftrightarrow n \neq 3$ when n is a natural number.
⊕ ⊻ ↮ ≢	U+2295 U+22BB U+21AE U+2262	⊕ ⊻ ↮ ≢ &oplus; &veebar; — &nequiv;	$\oplus$ \oplus $\veebar$ \veebar $\not \equiv$ \not\equiv	exclusive disjunction	xor, either ... or ... (but not both)	propositional logic, Boolean algebra	The statement $A\oplus B$ is true when either A or B, but not both, are true. This is equivalent to ¬(A ↔ B), hence the symbols $\nleftrightarrow$ and $\not \equiv$ .	$\lnot A\oplus A$ is always true and $A\oplus A$ is always false (if vacuous truth is excluded).
⊤ T 1	U+22A4	⊤ &top;	$\top$ \top	true (tautology)	top, truth, tautology, verum, full clause	propositional logic, Boolean algebra, first-order logic	$\top$ denotes a proposition that is always true.	The proposition $\top \lor P$ is always true since at least one of the two is unconditionally true.
⊥ F 0	U+22A5	⊥ &perp;	$\bot$ \bot	false (contradiction)	bottom, falsity, contradiction, falsum, empty clause	propositional logic, Boolean algebra, first-order logic	$\bot$ denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines.	The proposition $\bot \wedge P$ is always false since at least one of the two is unconditionally false.
∀ ()	U+2200	∀ ∀	$\forall$ \forall	universal quantification	given any, for all, for every, for each, for any	first-order logic	$\forall x$ $P(x)$ or $(x)$ $P(x)$ says “given any $x$ , $x$ has property $P$ .”	$\forall n\in \mathbb {N} :n^{2}\geq n.$
∃	U+2203	∃ ∃	$\exists$ \exists	existential quantification	there exists, for some	first-order logic	$\exists x$ $P(x)$ says “there exists an $x$ (at least one) such that $x$ has property $P$ .”	$\exists n\in \mathbb {N} :$ n is even.
∃!	U+2203 U+0021	∃ ! ∃!	$\exists !$ \exists !	uniqueness quantification	there exists exactly one	first-order logic (abbreviation)	$\exists !x$ $P(x)$ says “there exists exactly one $x$ such that $x$ has property $P$ .” Only $\forall$ and $\exists$ are part of formal logic. $\exists !x$ $P(x)$ is an abbreviation for $\exists x\forall y(P(y)\leftrightarrow y=x)$	$\exists !n\in \mathbb {N} :n+5=2n.$
( )	U+0028 U+0029	( ) ( )	$(~)$ ( )	precedence grouping	parentheses; brackets	almost all logic syntaxes, as well as metalanguage	Perform the operations inside the parentheses first.	$(8 \div 4) \div 2 = 2 \div 2 = 1$ , but $8 \div (4 \div 2) = 8 \div 2 = 4$ .
$\mathbb {D}$	U+1D53B	𝔻 &Dopf;	\mathbb{D}	domain of discourse	domain of discourse	metalanguage (first-order logic semantics)		$\mathbb {D} \mathbb {:} \mathbb {R}$
⊢	U+22A2	⊢ &vdash;	$\vdash$ \vdash	syntactic consequence	proves, syntactically entails (single) turnstile	metalanguage (metalogic)	$A\vdash B$ says “ $B$ is a theorem of $A$ ”. In other words, $A$ proves $B$ via a deductive system.	$(A\rightarrow B)\vdash (\lnot B\rightarrow \lnot A)$ (eg. by using natural deduction)
⊨	U+22A8	⊨ &vDash;	$\vDash$ \vDash, \models	semantic consequence or satisfaction	(semantically) entails or satisfies, models double turnstile	metalanguage (metalogic)	$A\vDash B$ says “in every model, it is not the case that $A$ is true and $B$ is false”. ${\mathcal {M}},\sigma \vDash B$ says a formula $B$ is true in a model ${\mathcal {M}}$ with variable assignment $\sigma$ .	$(A\rightarrow B)\vDash (\lnot B\rightarrow \lnot A)$ (eg. by using truth tables)
≡ ⟚ ⇔	U+2261 U+27DA U+21D4	≡ — ⇔ &equiv; — ⇔	$\equiv$ \equiv $\Leftrightarrow$ \Leftrightarrow	logical equivalence	is logically equivalent to	metalanguage (metalogic)	It’s when $A\vDash B$ and $B\vDash A$ . Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.	$(A\rightarrow B)\equiv (\lnot A\lor B)$
⊬	U+22AC		⊬\nvdash		does not syntactically entail (does not prove)	metalanguage (metalogic)	$A\nvdash B$ says “ $B$ is not a theorem of $A$ ”. In other words, $B$ is not derivable from $A$ via a deductive system.	$A\lor B\nvdash A\wedge B$
⊭	U+22AD		⊭\nvDash		does not semantically entail	metalanguage (metalogic)	$A\nvDash B$ says “ $A$ does not guarantee the truth of $B$ ”. In other words, $A$ does not make $B$ true.	$A\lor B\nvDash A\wedge B$
□	U+25A1		$\Box$ \Box	necessity (in a model)	box; it is necessary that	modal logic	modal operator for “it is necessary that” in alethic logic, “it is provable that” in provability logic, “it is obligatory that” in deontic logic, “it is believed that” in doxastic logic.	$\Box \forall xP(x)$ says “it is necessary that everything has property $P$ ”
◇	U+25C7		$\Diamond$ \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”).	$\Diamond \exists xP(x)$ says “it is possible that something has property $P$ ”
∴	U+2234		∴\therefore	therefore	therefore	metalanguage	abbreviation for “therefore”.
∵	U+2235		∵\because	because	because	metalanguage	abbreviation for “because”.
≔ ≜ ≝	U+2254 U+225C U+225D	≔ &coloneq;	≔ \coloneqq $:=$ := $\triangleq$ \triangleq ${\stackrel {\scriptscriptstyle \mathrm {def} }{=}}$ \stackrel{ \scriptscriptstyle \mathrm{def}}{=}	definition	is defined as	metalanguage	$a:=b$ means "from now on, $a$ is defined to be another name for $b$ ." This is a statement in the metalanguage, not the object language. The notation $a\equiv b$ may occasionally be seen in physics, meaning the same as $a:=b$ .	$\cosh x:={\frac {e^{x}+e^{-x}}{2}}$
↑ \| ⊼	U+2191 U+007C U+22BC		$\uparrow$ \uparrow	Sheffer stroke, NAND	NAND, not both up arrow	Propositional logic	NAND is the negation of conjunction so $A\uparrow B$ is true if and only if it's not the case that both $A$ and $B$ are true. See also NAND gate
↓ ⊽	U+2193 U+22BD		$\downarrow$ \downarrow	Peirce Arrow, NOR	nor down arrow	Propositional logic	NOR is the negation of disjunction so $A\downarrow B$ is true if and only if both $A$ and $B$ are false. See also NOR gate