قائمة الرموز المنطقية
في المنطق، تُستخدم مجموعة من الرموز للتعبير عن مفاهيمَ منطقيةٍ. القائمة الآتية تُلخّص أبرز الترميزات مع تسميتها واستعمالها في لغة HTML.[1]
الرمز | الاسم | وصف | مثال | قيمة اليونيكود
(في نظام العد الست عشري) |
قيمة HTML
(في نظام العد العشري) |
اسم ترميز HTML | ترميز اللاتخ
LaTeX |
---|---|---|---|---|---|---|---|
القراءة | |||||||
التصنيف | |||||||
⇒ → ⊃ |
قضية شرطية | is true if and only if can be true and can be false but not vice versa. 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). |
العبارة صحيحة. لكن العبارة خاطئة؛ لأنَّ ممكن أن تكون -2. | U+21D2 U+2192 U+2283 |
⇒ → ⊃ |
⇒ → ⊃ |
\Rightarrow
\to or \rightarrow\supset \implies |
يقتضي؛ إذا ... فإنَّ | |||||||
حساب القضايا، الجبر | |||||||
⇔ ≡ ↔ |
قضية تكافؤية | is true only if both and are false, or both and are true. | U+21D4 U+2261 U+2194 |
⇔ ≡ ↔ |
⇔ ≡ ↔ |
\Leftrightarrow
\equiv\leftrightarrow \iff | |
إذا وفقط إذا | |||||||
حساب القضايا | |||||||
¬ ˜ ! |
نفي | 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 | |
ليس | |||||||
حساب القضايا | |||||||
∧ · & |
logical conjunction | 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
\&[2] |
و | |||||||
حساب القضايا، جبر بول | |||||||
∨ + ∥ |
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 | |||||||
حساب القضايا، جبر بول | |||||||
⊕ ⊻ |
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 | |||||||
حساب القضايا، جبر بول | |||||||
⊤ T 1 |
Tautology | The statement ⊤ is unconditionally true. | A ⇒ ⊤ is always true. | U+22A4 |
⊤ |
\top | |
top, verum | |||||||
حساب القضايا، جبر بول | |||||||
⊥ 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 | |||||||
حساب القضايا، جبر بول | |||||||
∀ () |
universal quantification | ∀ x: P(x) or (x) P(x) means P(x) is true for all x. | ∀ n ∈ ℕ: n2 ≥ n. | U+2200 |
∀ |
∀ |
\forall |
for all; for any; for each | |||||||
منطق الرتبة الأولى | |||||||
∃ |
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 | |||||||
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. | U+2203 U+0021 | ∃ ! | \exists ! | |
there exists exactly one | |||||||
منطق الرتبة الأولى | |||||||
≔ ≡ :⇔ |
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 | |||||||
كل مكان | |||||||
( ) |
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 | |||||||
كل مكان | |||||||
⊢ |
Turnstile | x ⊢ y means y is provable from x (in some specified formal system). | A → B ⊢ ¬B → ¬A | U+22A2 | ⊢ | \vdash | |
provable | |||||||
حساب القضايا، منطق الرتبة الأولى | |||||||
⊨ |
double turnstile | x ⊨ y means x semantically entails y | A → B ⊨ ¬B → ¬A | U+22A8 | ⊨ | \vDash, \models | |
entails | |||||||
حساب القضايا، منطق الرتبة الأولى |
انظر أيضا
مراجع
- "Named character references". HTML 5.1 Nightly. W3C. مؤرشف من الأصل في 2016-01-28. اطلع عليه بتاريخ 2015-09-09.
- Although this character is available in LaTeX, the ميدياويكي TeX system does not support it.
- بوابة رياضيات
- بوابة فلسفة
- بوابة منطق
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