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# Template:Symbol/Logic

⧼Purge⧽ Template:Symbol/Logic

Issue: For the "end of proof mark," the LaTeX${\displaystyle \textstyle {\blacksquare }}$ (\blacksquare) isn't quite right, it should be like the HTML+CSS
 ∎
.

Logic symbols produced by the {{symbol}} template.
Code
{{sym|...}}
(see 3 rd column)
{{sym|...|hex}},
&#x{{sym|...|hex}};
Styled HTML+CSS
{{sym|...}}
in
{{math|...|&&}},
{{math|...|&}}
Code
{{sym|...|tex}}
Result
(TeX)
Rendered TeX
{{sym|...|tex}}
in
{{math|...|}},
{{math|...|\$}}
Code
{{sym|...|name}}
Name
Logic
{{sym|def}} 2254, ≔
 :=
,
 :=
{{sym|def|tex}} := ${\displaystyle {\begin{array}{l}\displaystyle {:=}\end{array}}}$,${\displaystyle \textstyle {:=}}$ {{sym|def|name}} [LHS term] is defined as [RHS]
{{sym|coleq}} 2254, ≔
 :=
,
 :=
{{sym|coleq|tex}} := ${\displaystyle {\begin{array}{l}\displaystyle {:=}\end{array}}}$,${\displaystyle \textstyle {:=}}$ {{sym|coleq|name}} [LHS term] is defined as [RHS]
{{sym|defines}} 2255, ≕
 =:
,
 =:
{{sym|defines|tex}} =: ${\displaystyle {\begin{array}{l}\displaystyle {=:}\end{array}}}$,${\displaystyle \textstyle {=:}}$ {{sym|defines|name}} [LHS] defines [RHS term]
{{sym|eqcol}} 2255, ≕
 =:
,
 =:
{{sym|eqcol|tex}} =: ${\displaystyle {\begin{array}{l}\displaystyle {=:}\end{array}}}$,${\displaystyle \textstyle {=:}}$ {{sym|eqcol|name}} [LHS] defines [RHS term]
{{sym|not}} 00AC, ¬
 ¬
,
 ¬
{{sym|not|tex}} {\lnot} ${\displaystyle {\begin{array}{l}\displaystyle {\lnot }\end{array}}}$,${\displaystyle \textstyle {\lnot }}$ {{sym|not|name}} logical not
{{sym|and}} 2227, ∧
 ∧
,
 ∧
{{sym|and|tex}} {\land} ${\displaystyle {\begin{array}{l}\displaystyle {\land }\end{array}}}$,${\displaystyle \textstyle {\land }}$ {{sym|and|name}} logical and
{{sym|And}} 22C0, ⋀
 ⋀
,
 ⋀
{{sym|And|tex}} \bigwedge ${\displaystyle {\begin{array}{l}\displaystyle {\bigwedge }\end{array}}}$,${\displaystyle \textstyle {\bigwedge }}$ {{sym|And|name}} n-ary logical and
{{sym|nand}} 2191, ↑
 ↑
,
 ↑
{{sym|nand|tex}} {\uparrow} ${\displaystyle {\begin{array}{l}\displaystyle {\uparrow }\end{array}}}$,${\displaystyle \textstyle {\uparrow }}$ {{sym|nand|name}} logical nand
{{sym|or}} 2228, ∨
 ∨
,
 ∨
{{sym|or|tex}} {\lor} ${\displaystyle {\begin{array}{l}\displaystyle {\lor }\end{array}}}$,${\displaystyle \textstyle {\lor }}$ {{sym|or|name}} logical or
{{sym|Or}} 22C1, ⋁
 ⋁
,
 ⋁
{{sym|Or|tex}} \bigvee ${\displaystyle {\begin{array}{l}\displaystyle {\bigvee }\end{array}}}$,${\displaystyle \textstyle {\bigvee }}$ {{sym|Or|name}} n-ary logical or
{{sym|nor}} 2193, ↓
 ↓
,
 ↓
{{sym|nor|tex}} {\downarrow} ${\displaystyle {\begin{array}{l}\displaystyle {\downarrow }\end{array}}}$,${\displaystyle \textstyle {\downarrow }}$ {{sym|nor|name}} logical nor
{{sym|xor}} 2295, ⊕
 ⊕
,
 ⊕
{{sym|xor|tex}} {\oplus} ${\displaystyle {\begin{array}{l}\displaystyle {\oplus }\end{array}}}$,${\displaystyle \textstyle {\oplus }}$ {{sym|xor|name}} logical xor
{{sym|imp}} 2192, →
 →
,
 →
{{sym|imp|tex}} {\rightarrow} ${\displaystyle {\begin{array}{l}\displaystyle {\rightarrow }\end{array}}}$,${\displaystyle \textstyle {\rightarrow }}$ {{sym|imp|name}} implies
{{sym|Imp}} 27F9, ⟹
 ⟹
,
 ⟹
{{sym|Imp|tex}} {\Rightarrow} ${\displaystyle {\begin{array}{l}\displaystyle {\Rightarrow }\end{array}}}$,${\displaystyle \textstyle {\Rightarrow }}$ {{sym|Imp|name}} implies
{{sym|imp by}} 2190, ←
 ←
,
 ←
{{sym|imp by|tex}} {\leftarrow} ${\displaystyle {\begin{array}{l}\displaystyle {\leftarrow }\end{array}}}$,${\displaystyle \textstyle {\leftarrow }}$ {{sym|imp by|name}} is implied by
{{sym|Imp by}} 27F8, ⟸
 ⟸
,
 ⟸
{{sym|Imp by|tex}} {\Leftarrow} ${\displaystyle {\begin{array}{l}\displaystyle {\Leftarrow }\end{array}}}$,${\displaystyle \textstyle {\Leftarrow }}$ {{sym|Imp by|name}} is implied by
{{sym|iff}} 2194, ↔
 ↔
,
 ↔
{{sym|iff|tex}} {\leftrightarrow} ${\displaystyle {\begin{array}{l}\displaystyle {\leftrightarrow }\end{array}}}$,${\displaystyle \textstyle {\leftrightarrow }}$ {{sym|iff|name}} if and only if
{{sym|Iff}} 27FA, ⟺
 ⟺
,
 ⟺
{{sym|Iff|tex}} {\Leftrightarrow} ${\displaystyle {\begin{array}{l}\displaystyle {\Leftrightarrow }\end{array}}}$,${\displaystyle \textstyle {\Leftrightarrow }}$ {{sym|Iff|name}} if and only if
{{sym|exist}} 2203, ∃
 ∃
,
 ∃
{{sym|exist|tex}} {\exists} ${\displaystyle {\begin{array}{l}\displaystyle {\exists }\end{array}}}$,${\displaystyle \textstyle {\exists }}$ {{sym|exist|name}} there exists
{{sym|exists}} 2203, ∃
 ∃
,
 ∃
{{sym|exists|tex}} {\exists} ${\displaystyle {\begin{array}{l}\displaystyle {\exists }\end{array}}}$,${\displaystyle \textstyle {\exists }}$ {{sym|exists|name}} there exists
{{sym|uexist}} 2203, ∃
 ∃!
,
 ∃!
{{sym|uexist|tex}} {\exists!} ${\displaystyle {\begin{array}{l}\displaystyle {\exists !}\end{array}}}$,${\displaystyle \textstyle {\exists !}}$ {{sym|uexist|name}} there exists exactly one
{{sym|uexists}} 2203, ∃
 ∃!
,
 ∃!
{{sym|uexists|tex}} {\exists!} ${\displaystyle {\begin{array}{l}\displaystyle {\exists !}\end{array}}}$,${\displaystyle \textstyle {\exists !}}$ {{sym|uexists|name}} there exists exactly one
{{sym|nexist}} 2204, ∄
 ∄
,
 ∄
{{sym|nexist|tex}} {\nexists} ${\displaystyle {\begin{array}{l}\displaystyle {\nexists }\end{array}}}$,${\displaystyle \textstyle {\nexists }}$ {{sym|nexist|name}} there does not exist
{{sym|nexists}} 2204, ∄
 ∄
,
 ∄
{{sym|nexists|tex}} {\nexists} ${\displaystyle {\begin{array}{l}\displaystyle {\nexists }\end{array}}}$,${\displaystyle \textstyle {\nexists }}$ {{sym|nexists|name}} there does not exist
{{sym|forall}} 2200, ∀
 ∀
,
 ∀
{{sym|forall|tex}} {\forall} ${\displaystyle {\begin{array}{l}\displaystyle {\forall }\end{array}}}$,${\displaystyle \textstyle {\forall }}$ {{sym|forall|name}} for all
{{sym|because}} 2235, ∵
 ∵
,
 ∵
{{sym|because|tex}} {\because} ${\displaystyle {\begin{array}{l}\displaystyle {\because }\end{array}}}$,${\displaystyle \textstyle {\because }}$ {{sym|because|name}} because
{{sym|there4}} 2234, ∴
 ∴
,
 ∴
{{sym|there4|tex}} {\therefore} ${\displaystyle {\begin{array}{l}\displaystyle {\therefore }\end{array}}}$,${\displaystyle \textstyle {\therefore }}$ {{sym|there4|name}} therefore
{{sym|therefore}} 2234, ∴
 ∴
,
 ∴
{{sym|therefore|tex}} {\therefore} ${\displaystyle {\begin{array}{l}\displaystyle {\therefore }\end{array}}}$,${\displaystyle \textstyle {\therefore }}$ {{sym|therefore|name}} therefore
{{sym|taut}} 22A4, ⊤
 ⊤
,
 ⊤
{{sym|taut|tex}} {\top} ${\displaystyle {\begin{array}{l}\displaystyle {\top }\end{array}}}$,${\displaystyle \textstyle {\top }}$ {{sym|taut|name}} tautology
{{sym|top}} 22A4, ⊤
 ⊤
,
 ⊤
{{sym|top|tex}} {\top} ${\displaystyle {\begin{array}{l}\displaystyle {\top }\end{array}}}$,${\displaystyle \textstyle {\top }}$ {{sym|top|name}} tautology
{{sym|cont}} 22A5, ⊥
 ⊥
,
 ⊥
{{sym|cont|tex}} {\bot} ${\displaystyle {\begin{array}{l}\displaystyle {\bot }\end{array}}}$,${\displaystyle \textstyle {\bot }}$ {{sym|cont|name}} contradiction
{{sym|bot}} 22A5, ⊥
 ⊥
,
 ⊥
{{sym|bot|tex}} {\bot} ${\displaystyle {\begin{array}{l}\displaystyle {\bot }\end{array}}}$,${\displaystyle \textstyle {\bot }}$ {{sym|bot|name}} contradiction
{{sym|QED}} 220E, ∎
 ∎
,
 ∎
{{sym|QED|tex}} {\blacksquare} ${\displaystyle {\begin{array}{l}\displaystyle {\blacksquare }\end{array}}}$,${\displaystyle \textstyle {\blacksquare }}$ {{sym|QED|name}} end of proof (solid square)
{{sym|hollow QED}} 25A1, □
 □
,
 □
{{sym|hollow QED|tex}} {\square} ${\displaystyle {\begin{array}{l}\displaystyle {\square }\end{array}}}$,${\displaystyle \textstyle {\square }}$ {{sym|hollow QED|name}} end of proof (hollow square)