Logic symbols

In logic, a basic set of logic symbols is used as a shorthand for logical constructions. As these symbols are often considered as familiar, they are not always explained. For convenience, the following table lists some 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.

Note: This article contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of 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	⇒ → ⊃	$\Rightarrow$\Rightarrow $\to$\to $\supset$\supset
	implies; if .. then
	propositional logic, Heyting algebra
⇔ ≡ ↔	material equivalence	A ⇔ B means A is true if and only if B is true.	x + 5 = y +2  ⇔  x + 3 = y	U+21D4 U+2261 U+2194	⇔ ≡ ↔	$\Leftrightarrow$\Leftrightarrow $\equiv$\equiv $\leftrightarrow$\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	¬ ˜ ~	$\lnot$\lnot $\sim$\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;	$\wedge$\wedge or \land \&
	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;	$\lor$\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;	$\oplus$\oplus $\veebar$\veebar
	xor
	propositional logic, Boolean algebra
⊤ T 1	Tautology	The statement ⊤ is unconditionally true.	A ⇒ ⊤ is always true.	U+22A4	T	$\top$\top
	top
	propositional logic, Boolean algebra
⊥ F 0	Contradiction	The statement ⊥ is unconditionally false.	⊥ ⇒ A is always true.	U+22A5	&perp; F	$\bot$\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;	$\forall$\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;	$\exists$\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; !	$\exists !$\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+2261 U+003A U+229C	:= : &equiv; &hArr;	$:=$:= $\equiv$\equiv $\Leftrightarrow$\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		$\vdash$\vdash
	infers or is derived from
	propositional logic, first-order logic

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