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

=>
> ? 
material implication  implies; if ... then  propositional logic, Heyting algebra  is false when A is true and B is false but true otherwise.^{[2]}^{[circular reference]} 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+21D2 U+2192 U+2283 
⇒ → ⊃ 
⇒ → ⊃ 
\Rightarrow
\to or \rightarrow \supset \implies 
? ⟷ 
material equivalence  if and only if; iff; means the same as  propositional logic  is true only if both A and B are false, or both A and B are true.  U+21D4 U+2261 U+27F7 
⇔ ≡ ⟷ 
⇔ ≡ ⟷ 
\Leftrightarrow \equiv \leftrightarrow \iff  
¬
~ ! 
negation  not  propositional logic  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+00AC U+02DC U+0021 
¬ ˜ ! 
¬ ˜ ! 
\lnot or \neg
 
Domain of discourse  Domain of predicate  Predicate (mathematical logic)  U+1D53B  𝔻  𝔻  \mathbb{D}  
?
· & 
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 ? n >2 n = 3 when n is a natural number.  U+2227 U+00B7 U+0026 
∧ · & 
∧ · & 
\wedge or \land
\cdot \&^{[3]} 
?
+ ? 
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 n ? 3 when n is a natural number.  U+2228 U+002B U+2225 
∨ + ∥ 
∨

\lor or \vee

? ? ? 
exclusive disjunction  xor; either ... or  propositional logic, Boolean algebra  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

? T 1 ? 
Tautology  top, truth, full clause  propositional logic, Boolean algebra, firstorder logic  The statement ? is unconditionally true.  ?(A) => A is always true.  U+22A4 U+25A0 
⊤ 
⊤

\top 
? F 0 ? 
Contradiction  bottom, falsum, falsity, empty clause  propositional logic, Boolean algebra, firstorder logic  The statement ? is unconditionally false. (The symbol ? may also refer to perpendicular lines.)  ?(A) => A is always false.  U+22A5 U+25A1 
⊥ 
⊥ 
\bot 
?

universal quantification  for all; for any; for each  firstorder logic  ? x: P(x) or (x) P(x) means P(x) is true for all x.  U+2200 
∀ 
∀ 
\forall  
?

existential quantification  there exists  firstorder logic  ? x: P(x) means there is at least one x such that P(x) is true.  n is even.  U+2203  ∃  ∃  \exists 
?!

uniqueness quantification  there exists exactly one  firstorder logic  ?! x: P(x) means there is exactly one x such that P(x) is true.  U+2203 U+0021  ∃ !  ∃!  \exists !  
?
? : 
definition  is defined as  everywhere  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. 
A XOR B : (A ? B) ? ¬(A ? B) 
U+2254 (U+003A U+003D) U+2261 U+003A U+229C 
≔ (: =)

≔

:=
:\Leftrightarrow 
( )

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+0028 U+0029  ( )  (
) 
( ) 
?

turnstile  proves  propositional logic, firstorder logic  x ? y means x proves (syntactically entails) y  (A > B) ? (¬B > ¬A)  U+22A2  ⊢  ⊢  \vdash 
?

double turnstile  models  propositional logic, firstorder logic  x ? y means x models (semantically entails) y  (A > B) ? (¬B > ¬A)  U+22A8  ⊨  ⊨  \vDash, \models 
These symbols are sorted by their Unicode value:
The following operators are rarely supported by natively installed fonts.
As of 2014^{[update]} in Poland, the universal quantifier is sometimes written , and the existential quantifier as .^{[7]}^{[8]} The same applies for Germany.^{[9]}^{[10]}
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%".