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 value (decimal) 
HTML entity (named) 
LaTeX symbol 
Logic Name  Read as  Category  Explanation  Examples 

⇒
→ ⊃ 
U+21D2 U+2192 U+2283 
⇒ → ⊃ 
⇒ → ⊃ 
\Rightarrow
\implies \to or \rightarrow \supset 
material conditional (material implication)  implies, if ... then ..., it is not the case that ... and not ... 
propositional logic, Boolean algebra, Heyting algebra  is false when A is true and B is false but true otherwise. 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 x could be −2). 
⇔
↔ ≡ 
U+21D4 U+2194 U+2261 
⇔ ↔ ≡ 
⇔ ↔ ≡ 
\Leftrightarrow \iff \leftrightarrow \equiv 
material biconditional (material equivalence)  if and only if, iff, xnor  propositional logic, Boolean algebra  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, it depends on the author’s style.  
¬
~ ! 
U+00AC U+007E U+0021 
¬ ˜ ! 
¬ ˜ ! 
\lnot or \neg \sim 
negation  not  propositional logic, Boolean algebra  The statement is true if and only if A is false. A slash placed through another operator is the same as placed in front. 

∧
· & 
U+2227 U+00B7 U+0026 
∧ · & 
∧ · & 
\wedge or \land
\cdot \&^{[2]} 
logical conjunction  and  propositional logic, Boolean algebra  The statement A ∧ B is true if A and B are both true; otherwise, it is false.  
∨
+ ∥ 
U+2228 U+002B U+2225 
∨ + ∥ 
∨ + ∥ 
\lor or \vee \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 ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number.

⊻
⊕ ↮ ≢ 
U+22BB U+2295 U+21AE U+2262 
⊻ ⊕ ↮ ≢ 
⊻ ⊕ ≢ 
\veebar \oplus \not\equiv 
exclusive disjunction  xor, either ... or ... (but not both) 
propositional logic, Boolean algebra  The statement A ⊻ B is true when either A or B, but not both, are true. This is equivalent to ¬(A ↔ B), hence the symbols and . 

⊤
T 1 
U+22A4 
⊤ 
⊤ 
\top 
true (tautology)  top, truth, tautology, verum, full clause  propositional logic, Boolean algebra, firstorder logic  denotes a proposition that is always true.  The proposition is always true since at least one of the two is unconditionally true.

⊥
F 0 
U+22A5 
⊥ 
⊥ 
\bot 
false (contradiction)  bottom, falsity, contradiction, falsum, empty clause  propositional logic, Boolean algebra, firstorder logic  denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. 
The proposition is always false since at least one of the two is unconditionally false.

∀
() 
U+2200 
∀ 
∀ 
\forall 
universal quantification  given any, for all, for every, for each, for any  firstorder logic  or says “given any , has property .” 

∃

U+2203  ∃  ∃  \exists  existential quantification  there exists  firstorder logic  says “there exists an x (at least one) such that has property .”  n is even.

∃!

U+2203 U+0021  ∃ !  ∃!  \exists !  uniqueness quantification  there exists exactly one  firstorder logic  says “there exists exactly one x such that x has property P.” Only and are part of formal logic. is a shorthand for 

( )

U+0028 U+0029  ( )  ( ) 
( )  precedence grouping  parentheses; brackets  everywhere  Perform the operations inside the parentheses first.  (8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1, but 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4.

U+1D53B  𝔻  𝔻  \mathbb{D}  domain of discourse  domain of discourse  firstorder logic (semantics)  
⊢

U+22A2  ⊢  ⊢  \vdash  turnstile  syntactically entails (proves)  metalogic  says “ is a theorem of ”. In other words, proves via a deductive system. 

⊨

U+22A8  ⊨  ⊨  \vDash, \models  double turnstile  semantically entails  metalogic  says “in every model, it is not the case that is true and is false”. 

≡
⟚ ⇔ 
U+2261 U+27DA U+21D4 
≡ ⇔ 
≡ ⇔ 
\equiv \Leftrightarrow 
logical equivalence  is logically equivalent to  metalogic  It’s when and . Whether a symbol means a material biconditional or a logical equivalence, it depends on the author’s style.  
⊬

U+22AC  ⊬\nvdash  does not syntactically entail (does not prove)  metalogic  says “ is not a theorem of ”. In other words, is not derivable from via a deductive system. 

⊭

U+22AD  ⊭\nvDash  does not semantically entail  metalogic  says “ does not guarantee the truth of ”. In other words, does not make true. 

□

U+25A1  \Box  logical necessity within 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. 
says “it is necessary that everything has property P”
 
◇

U+25C7  \Diamond  logical possibility within 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”).  says “it is possible that something has property P”
 
∴

U+2234  ∴\therefore  therefore  therefore  informal metalanguage  shorthand for “therefore”.  
∵

U+2235  ∵\because  because  because  informal metalanguage  shorthand for “because”.  
≔
≡ 
U+2254 (U+003A U+003D) U+2261 
≔ (: =)

≔

:=

definition (between terms)  is defined as  informal metalanguage  (or ) means is defined to be another name for . This notation seems to have its origin in coding. However, from the standpoint of formal logic, there is no difference between and , since equality is a symmetric relation. 
These symbols are sorted by their Unicode value:
Symbol  Unicode value (hexadecimal) 
HTML value (decimal) 
HTML entity (named) 
LaTeX symbol 
Logic Name  Read as  Category  Explanation  Examples 

̅

U+0305  COMBINING OVERLINE  used format for denoting Gödel numbers.
denoting negation used primarily in electronics. 
using HTML style “4̅” is a shorthand for the standard numeral “SSSS0”.
“A ∨ B” says the Gödel number of “(A ∨ B)”. “A ∨ B” is the same as “¬(A ∨ B)”.  
↑
 
U+2191 U+007C 
UPWARDS ARROW VERTICAL LINE 
Sheffer stroke, the sign for the NAND operator (negation of conjunction). 

↓

U+2193  DOWNWARDS ARROW  Peirce Arrow, the sign for the NOR operator (negation of disjunction). 

⊙

U+2299  \odot  CIRCLED DOT OPERATOR  the sign for the XNOR operator (negation of exclusive disjunction).  
∁

U+2201  COMPLEMENT  
∄

U+2204  ∄\nexists  THERE DOES NOT EXIST  strike out existential quantifier, same as “¬∃”  
⊧

U+22A7  MODELS  is a model of (or “is a valuation satisfying”)  
†

U+2020  DAGGER  it is true that ...  Affirmation operator  
⊼

U+22BC  NAND  NAND operator  
⊽

U+22BD  NOR  NOR operator  
⋆

U+22C6  STAR OPERATOR  usually used for adhoc operators  
⊥
↓ 
U+22A5 U+2193 
UP TACK DOWNWARDS ARROW 
Webboperator or Peirce arrow, the sign for NOR. Confusingly, “⊥” is also the sign for contradiction or absurdity. 

⌐

U+2310  REVERSED NOT SIGN  
⌜
⌝ 
U+231C U+231D 
\ulcorner
\urcorner 
TOP LEFT CORNER TOP RIGHT CORNER 
corner quotes, also called “Quine quotes”; for quasiquotation, i.e. quoting specific context of unspecified (“variable”) expressions;^{[3]} also used for denoting Gödel number;^{[4]} 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+27DA  LEFT AND RIGHT DOUBLE TURNSTILE  semantic equivalent  
⟛

U+27DB  LEFT AND RIGHT TACK  syntactic equivalent  
⊩

U+22A9  FORCES  one of this symbol’s uses is to mean “models” in modal logic, as in 𝔐, 𝑤 ⊩ 𝑃 .  
⟡

U+27E1  WHITE CONCAVESIDED DIAMOND  never  modal operator  
⟢

U+27E2  WHITE CONCAVESIDED DIAMOND WITH LEFTWARDS TICK  was never  modal operator  
⟣

U+27E3  WHITE CONCAVESIDED 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+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 of Rosser's trick) The fish hook is also used as strict implication by C.I.Lewis ⥽ . See here for an image of glyph. Added to Unicode 3.2.0.  
⨇

U+2A07  TWO LOGICAL AND OPERATOR 
As of 2014^{[update]} in Poland, the universal quantifier is sometimes written , and the existential quantifier as ^{[citation needed]}. The same applies for Germany^{[citation needed]}.
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%".