List of logic symbols
Basic logic symbols

List of logic symbols

Section Title: Basic logic symbols
Table Section Text: None

Symbol	Name	Explanation	Examples	Unicode value (hexadecimal)	HTML value (decimal)	HTML entity (named)	LaTeX symbol

Read as

Category

⇒ → ⊃	material implication	is true if and only if can be true and can be false but not vice versa . may mean the same as (the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols).	is true, but is in general false (since could be −2).	U+21D2 U+2192 U+2283	⇒ → ⊃	⇒ → ⊃	\Rightarrow \to or \rightarrow \supset \implies

implies; if .. then

propositional logic, Heyting algebra

⇔ ≡ ↔	material equivalence	is true only if both and are false, or both and are true.	U+21D4 U+2261 U+2194	⇔ ≡ ↔	⇔ ≡ ↔	\Leftrightarrow \equiv \leftrightarrow \iff

if and only if; iff; means the same as

propositional logic

¬ ˜ !	negation	The statement is true if and only if is false. A slash placed through another operator is the same as placed in front.	U+00AC U+02DC U+0021	¬ ˜ !	¬ ˜ !	\lnot or \neg \sim

not

propositional logic

∧ · &	logical conjunction	The statement A ∧ B is true if A and B are both true; otherwise, it is false.	n 2 ⇔ n = 3 when n is a natural number.	U+2227 U+00B7 U+0026	∧ · &	∧ · &	\wedge or \land \&

and

propositional logic, Boolean algebra

∨ + ∥	logical (inclusive) 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 U+002B U+2225	∨ + ∥	∨	\lor or \vee \parallel

or

propositional logic, Boolean algebra

⊕ ⊻	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, and A ⊕ A always false, if vacuous truth is excluded.	U+2295 U+22BB	⊕ ⊻	⊕	\oplus \veebar

xor

propositional logic, Boolean algebra

⊤ T 1	Tautology	The statement ⊤ is unconditionally true.	A ⇒ ⊤ is always true.	U+22A4	⊤	\top

top, verum

propositional logic, Boolean algebra

⊥ F 0	Contradiction	The statement ⊥ is unconditionally false. (The symbol ⊥ may also refer to perpendicular lines.)	⊥ ⇒ A is always true.	U+22A5	⊥	⊥	\bot

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 ∈ ℕ: n2 ≥ n.	U+2200	∀	∀	\forall

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: n is even.	U+2203	∃	∃	\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	∃ !	\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).	cosh x ≔ (1/2)(exp x + exp (−x)) A XOR B :⇔ (A ∨ B) ∧ ¬(A ∧ B)	U+2254 (U+003A U+003D) U+2261 U+003A U+229C	≔ (: =) ≡ ⊜	≡ ⇔	:= \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	( )	( )

parentheses, brackets

everywhere

⊢	Turnstile	x ⊢ y means y is provable from x (in some specified formal system).	A → B ⊢ ¬B → ¬A	U+22A2	⊢	\vdash

provable

propositional logic, first-order logic

⊨	double turnstile	x ⊨ y means x semantically entails y	A → B ⊨ ¬B → ¬A	U+22A8	⊨	\vDash, \models

entails

propositional logic, first-order logic

Sentence(s)

The negation can be read as "not ".

final_sentence: The negation can be read as "not ".