Template:Symbol/Logic

⧼Purge⧽ Template:Symbol/Logic

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