In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols together with their name, pronunciation, and the related field of mathematics. Additionally, the third column contains an informal definition, the fourth column gives a short example, the fifth and sixth give the unicode location and name for use in HTML documents.^{[1]} The last column provides the LaTeX symbol.
Symbol

Name  Explanation  Examples  Unicode Value (hexdecimal) 
HTML Value (decimal) 
HTML Entity (named) 
LaTeX symbol 

Read as  
Category  
⇒
→ ⊃ 
material implication  is true only in the case that either is false or is true. 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). 
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  
Symbol

Name  Explanation  Examples  Unicode Value (hexdecimal) 
HTML Value (decimal) 
HTML Entity (named) 
LaTeX symbol 
Read as  
Category  
∧
· & 
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+00B7 U+0026 
∧ · & 
∧ · & 
\wedge or \land
\&^{[2]} 
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  
Symbol

Name  Explanation  Examples  Unicode Value (hexdecimal) 
HTML Value (decimal) 
HTML Entity (named) 
LaTeX symbol 
Read as  
Category  
⊥ 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: n^{2} ≥ n.  U+2200 
∀ 
∀ 
\forall 
for all; for any; for each  
firstorder 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  
firstorder 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  
firstorder logic  
Symbol

Name  Explanation  Examples  Unicode Value (hexdecimal) 
HTML Value (decimal) 
HTML Entity (named) 
LaTeX symbol 
Read as  
Category  
≔
≡ :⇔ 
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 :\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, firstorder logic  
⊨

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

Name  Explanation  Examples  Unicode Value (hexdecimal) 
HTML Value (decimal) 
HTML Entity (named) 
LaTeX symbol 
Read as  
Category 
These symbols are sorted by their Unicode value:
<span style="textdecoration: overline">∧</span>
: ∧<span style="textdecoration: overline">∨</span>
: ∨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.
As of 2014^{[update]} in Poland, the universal quantifier is sometimes written and the existential quantifier as .^{[citation needed]} The same applies for Germany.^{[6]}
The ⇒ symbol is often used in text to mean "result" or "conclusion", as in "We examined whether to sell the product ⇒ We will not sell it". Also, the → symbol is often used to denote "changed to" as in the sentence "The interest rate changed. March 20% → April 21%".
We turn now to the second of our connective symbols, the centered dot, which is called the conjunction sign.
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