Logic symbols
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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 ⇒ x^{2} = 4 is true, but x^{2} = 4 ⇒ x = 2 is in general false (since x could be −2).  U+21D2 U+2192 U+2283 
⇒ → ⊃ 
\Rightarrow
\to \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
\equiv \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
\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 
∧ & 
\wedge or \land \&^{[1]} 
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  ∨  \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 \veebar 
xor  
propositional logic, Boolean algebra  
⊤ T 1 
Tautology  The statement ⊤ is unconditionally true.  A ⇒ ⊤ is always true.  U+22A4  T  \top 
top  
propositional logic, Boolean algebra  
⊥ F 0 
Contradiction  The statement ⊥ is unconditionally false.  ⊥ ⇒ A is always true.  U+22A5  ⊥ F 
\bot 
bottom  
propositional logic, Boolean algebra  
∀

universal quantification  ∀ 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  
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  ∃  \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  
:=
≡ :⇔ 
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  ( )  ( ) 
everywhere  
⊢

inference  x ⊢ y means y is derived from x.  A → B ⊢ ¬B → ¬A  U+22A2  \vdash  
infers or is derived from  
propositional logic, firstorder logic 