Table of logic symbols
From Wikipedia, the free encyclopedia
In logic, a set of symbols is frequently used to express logical constructs. As logicians are familiar with these symbols, they are not explained each time they are used. So, for students of logic, the following table lists many 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, in some cases, different symbols have the same meaning, and the same symbol has, depending on the context, different meanings.
- Note: This article contains special characters.
[edit] Basic logic symbols
|
Symbol
|
Name | Explanation | Examples | Unicode Value |
|---|---|---|---|---|
| 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). | 8658 8594 8835 |
| implies; if .. then | ||||
| propositional logic | ||||
|
⇔
↔ |
material equivalence | A ⇔ B means A is true if B is true and A is false if B is false. | x + 5 = y +2 ⇔ x + 3 = y | 8660 8596 |
| if and only if; iff | ||||
| propositional logic | ||||
|
¬
˜ |
logical 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) |
172 732 |
| 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 and an integer. | 8743 38 |
| 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. | 8744 |
| or | ||||
| propositional logic | ||||
⊕
⊻
|
exclusive or | 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. | 8853 8891 |
| xor | ||||
| propositional logic, Boolean algebra | ||||
|
∀
|
universal quantification | ∀ x: P(x) means P(x) is true for all x. | ∀ n ∈ N: n2 ≥ n. | 8704 |
| 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. | 8707 |
| 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. | 8707 33 |
| 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) |
58 61 8801 58 8660 |
| 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. | 40 41 |
| everywhere | ||||
|
⊢
|
inference | x ⊢ y means y is derived from x. | A → B ⊢ ¬B → ¬A | 8866 |
| infers or is derived from | ||||
| propositional logic, first-order logic |
[edit] See also
[edit] Special characters
Technical note: Due to technical limitations, most computers would not display some special characters in this article. Such characters may be rendered as boxes, question marks, or other nonsense symbols, depending on your browser, operating system, and installed fonts. Even if you have ensured that your browser is interpreting the article as UTF-8 encoded and you have installed a font that supports a wide range of Unicode, such as Code2000, Arial Unicode MS, Lucida Sans Unicode or one of the free software Unicode fonts, you may still need to use a different browser, as browser capabilities in this regard tend to vary.
