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6,898 bytes added ,  03:25, 30 October 2015
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A '''truth table''' is a tabular array that illustrates the computation of a [[boolean function]], that is, a function of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{B}</math> is the [[boolean domain]] <math>\{ 0, 1 \}.\!</math>
+
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
 +
 
 +
A '''truth table''' is a tabular array that illustrates the computation of a ''logical function'', that is, a function of the form <math>f : \mathbb{A}^k \to \mathbb{A},</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{A}</math> is the domain of logical values <math>\{ \operatorname{false}, \operatorname{true} \}.</math>  The names of the logical values, or ''truth values'', are commonly abbreviated in accord with the equations <math>\operatorname{F} = \operatorname{false}</math> and <math>\operatorname{T} = \operatorname{true}.</math>
 +
 
 +
In many applications it is usual to represent a truth function by a [[boolean function]], that is, a function of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{B}</math> is the [[boolean domain]] <math>\{ 0, 1 \}.\!</math> In most applications <math>\operatorname{false}</math> is represented by <math>0\!</math> and <math>\operatorname{true}</math> is represented by <math>1\!</math> but the opposite representation is also possible, depending on the overall representation of truth functions as boolean functions.  The remainder of this article assumes the usual representation, taking the equations <math>\operatorname{F} = 0</math> and <math>\operatorname{T} = 1</math> for granted.
    
==Logical negation==
 
==Logical negation==
   −
'''[[Logical negation]]''' is an [[logical operation|operation]] on one [[logical value]], typically the value of a [[proposition]], that produces a value of ''true'' when its operand is false and a value of ''false'' when its operand is true.
+
'''[[Logical negation]]''' is an operation on one logical value, typically the value of a proposition, that produces a value of ''true'' when its operand is false and a value of ''false'' when its operand is true.
   −
The truth table of '''NOT p''' (also written as '''~p''' or '''&not;p''') is as follows:
+
The truth table of <math>\operatorname{NOT}~ p,</math> also written <math>\lnot p,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:40%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Negation'''
+
|+ style="height:30px" | <math>\text{Logical Negation}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:20%" | p
+
| style="width:50%" | <math>p\!</math>
! style="width:20%" | &not;p
+
| style="width:50%" | <math>\lnot p\!</math>
 
|-
 
|-
| F || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|}
 
|}
    
<br>
 
<br>
   −
The logical negation of a proposition '''p''' is notated in different ways in various contexts of discussion and fields of application.  Among these variants are the following:
+
The negation of a proposition <math>p\!</math> may be found notated in various ways in various contexts of application, often merely for typographical convenience.  Among these variants are the following:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; width:40%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" width="45%"
|+ '''Variant Notations'''
+
|+ style="height:30px" | <math>\text{Variant Notations}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="text-align:center" | Notation
+
| width="50%" align="center" | <math>\text{Notation}\!</math>
! Vocalization
+
| width="50%" | <math>\text{Vocalization}\!</math>
 +
|-
 +
| align="center" | <math>\bar{p}\!</math>
 +
| <math>p\!</math> bar
 
|-
 
|-
| style="text-align:center" | <math>\bar{p}</math>
+
| align="center" | <math>\tilde{p}\!</math>
| bar ''p''
+
| <math>p\!</math> tilde
 
|-
 
|-
| style="text-align:center" | <math>p'\!</math>
+
| align="center" | <math>p'\!</math>
| ''p'' prime,<p> ''p'' complement
+
| <math>p\!</math> prime<br> <math>p\!</math> complement
 
|-
 
|-
| style="text-align:center" | <math>!p\!</math>
+
| align="center" | <math>!p\!</math>
| bang ''p''
+
| bang <math>p\!</math>
 
|}
 
|}
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==Logical conjunction==
 
==Logical conjunction==
   −
'''[[Logical conjunction]]''' is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both of its operands are true.
+
'''[[Logical conjunction]]''' is an operation on two logical values, typically the values of two propositions, that produces a value of ''true'' if and only if both of its operands are true.
   −
The truth table of '''p AND q''' (also written as '''p &and; q''', '''p & q''', or '''p<math>\cdot</math>q''') is as follows:
+
The truth table of <math>p ~\operatorname{AND}~ q,</math> also written <math>p \land q\!</math> or <math>p \cdot q,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Conjunction'''
+
|+ style="height:30px" | <math>\text{Logical Conjunction}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
+
| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
+
| style="width:33%" | <math>q\!</math>
! style="width:15%" | p &and; q
+
| style="width:33%" | <math>p \land q</math>
 
|-
 
|-
| F || F || F
+
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| F || T || F
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || F || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || T || T
+
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|}
 
|}
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==Logical disjunction==
 
==Logical disjunction==
   −
'''[[Logical disjunction]]''', also called '''logical alternation''', is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are false.
+
'''[[Logical disjunction]]''', also called '''logical alternation''', is an operation on two logical values, typically the values of two propositions, that produces a value of ''false'' if and only if both of its operands are false.
   −
The truth table of '''p OR q''' (also written as '''p &or; q''') is as follows:
+
The truth table of <math>p ~\operatorname{OR}~ q,</math> also written <math>p \lor q,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Disjunction'''
+
|+ style="height:30px" | <math>\text{Logical Disjunction}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
+
| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
+
| style="width:33%" | <math>q\!</math>
! style="width:15%" | p &or; q
+
| style="width:33%" | <math>p \lor q</math>
 
|-
 
|-
| F || F || F
+
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| F || T || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || F || T
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || T || T
+
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|}
 
|}
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==Logical equality==
 
==Logical equality==
   −
'''[[Logical equality]]''' is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both operands are false or both operands are true.
+
'''[[Logical equality]]''' is an operation on two logical values, typically the values of two propositions, that produces a value of ''true'' if and only if both operands are false or both operands are true.
   −
The truth table of '''p EQ q''' (also written as '''p = q''', '''p &harr; q''', or '''p &equiv; q''') is as follows:
+
The truth table of <math>p ~\operatorname{EQ}~ q,</math> also written <math>p = q,\!</math> <math>p \Leftrightarrow q,\!</math> or <math>p \equiv q,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Equality'''
+
|+ style="height:30px" | <math>\text{Logical Equality}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
+
| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
+
| style="width:33%" | <math>q\!</math>
! style="width:15%" | p = q
+
| style="width:33%" | <math>p = q\!</math>
 
|-
 
|-
| F || F || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| F || T || F
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || F || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || T || T
+
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|}
 
|}
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==Exclusive disjunction==
 
==Exclusive disjunction==
   −
'''[[Exclusive disjunction]]''', also known as '''logical inequality''' or '''symmetric difference''', is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' just in case exactly one of its operands is true.
+
'''[[Exclusive disjunction]]''', also known as '''logical inequality''' or '''symmetric difference''', is an operation on two logical values, typically the values of two propositions, that produces a value of ''true'' just in case exactly one of its operands is true.
   −
The truth table of '''p XOR q''' (also written as '''p + q''', '''p &oplus; q''', or '''p &ne; q''') is as follows:
+
The truth table of <math>p ~\operatorname{XOR}~ q,</math> also written <math>p + q\!</math> or <math>p \ne q,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Exclusive Disjunction'''
+
|+ style="height:30px" | <math>\text{Exclusive Disjunction}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
+
| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
+
| style="width:33%" | <math>q\!</math>
! style="width:15%" | p XOR q
+
| style="width:33%" | <math>p ~\operatorname{XOR}~ q</math>
 
|-
 
|-
| F || F || F
+
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| F || T || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || F || T
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || T || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|}
 
|}
    
<br>
 
<br>
   −
The following equivalents can then be deduced:
+
The following equivalents may then be deduced:
   −
: <math>\begin{matrix}
+
{| align="center" cellspacing="10" width="90%"
p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\
+
|
\\
+
<math>\begin{matrix}
       & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\
+
p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q)
\\
+
\\[6pt]
 +
       & = & (p \lor q) & \land & (\lnot p \lor \lnot q)
 +
\\[6pt]
 
       & = & (p \lor q) & \land & \lnot (p \land q)
 
       & = & (p \lor q) & \land & \lnot (p \land q)
 
\end{matrix}</math>
 
\end{matrix}</math>
 +
|}
    
==Logical implication==
 
==Logical implication==
   −
The '''[[logical implication]]''' and the '''[[material conditional]]''' are both associated with an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if the first operand is true and the second operand is false.
+
The '''[[logical implication]]''' relation and the '''material conditional''' function are both associated with an operation on two logical values, typically the values of two propositions, that produces a value of ''false'' if and only if the first operand is true and the second operand is false.
   −
The truth table associated with the material conditional '''if p then q''' (symbolized as '''p&nbsp;&rarr;&nbsp;q''') and the logical implication '''p implies q''' (symbolized as '''p&nbsp;&rArr;&nbsp;q''') is as follows:
+
The truth table associated with the material conditional <math>\text{if}~ p ~\text{then}~ q,\!</math> symbolized <math>p \rightarrow q,\!</math> and the logical implication <math>p ~\text{implies}~ q,\!</math> symbolized <math>p \Rightarrow q,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Implication'''
+
|+ style="height:30px" | <math>\text{Logical Implication}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
+
| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
+
| style="width:33%" | <math>q\!</math>
! style="width:15%" | p &rArr; q
+
| style="width:33%" | <math>p \Rightarrow q\!</math>
 
|-
 
|-
| F || F || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| F || T || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || F || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || T || T
+
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|}
 
|}
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==Logical NAND==
 
==Logical NAND==
   −
The '''[[logical NAND]]''' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are true.  In other words, it produces a value of ''true'' if and only if at least one of its operands is false.
+
The '''[[logical NAND]]''' is an operation on two logical values, typically the values of two propositions, that produces a value of ''false'' if and only if both of its operands are true.  In other words, it produces a value of ''true'' if and only if at least one of its operands is false.
   −
The truth table of '''p NAND q''' (also written as '''p&nbsp;|&nbsp;q''' or '''p&nbsp;&uarr;&nbsp;q''') is as follows:
+
The truth table of <math>p ~\operatorname{NAND}~ q,</math> also written <math>p \stackrel{\circ}{\curlywedge} q\!</math> or <math>p \barwedge q,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical NAND'''
+
|+ style="height:30px" | <math>\text{Logical NAND}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
+
| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
+
| style="width:33%" | <math>q\!</math>
! style="width:15%" | p &uarr; q
+
| style="width:33%" | <math>p \stackrel{\circ}{\curlywedge} q\!</math>
 
|-
 
|-
| F || F || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| F || T || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || F || T
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| T || T || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|}
 
|}
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==Logical NNOR==
 
==Logical NNOR==
   −
The '''[[logical NNOR]]''' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both of its operands are false.  In other words, it produces a value of ''false'' if and only if at least one of its operands is true.
+
The '''[[logical NNOR]]''' (&ldquo;Neither Nor&rdquo;) is an operation on two logical values, typically the values of two propositions, that produces a value of ''true'' if and only if both of its operands are false.  In other words, it produces a value of ''false'' if and only if at least one of its operands is true.
   −
The truth table of '''p NNOR q''' (also written as '''p&nbsp;&perp;&nbsp;q''' or '''p&nbsp;&darr;&nbsp;q''') is as follows:
+
The truth table of <math>p ~\operatorname{NNOR}~ q,</math> also written <math>p \curlywedge q,\!</math> appears below:
    
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical NNOR'''
+
|+ style="height:30px" | <math>\text{Logical NNOR}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
+
| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
+
| style="width:33%" | <math>q\!</math>
! style="width:15%" | p &darr; q
+
| style="width:33%" | <math>p \curlywedge q\!</math>
 
|-
 
|-
| F || F || T
+
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| F || T || F
+
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || F || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || T || F
+
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|}
 
|}
    
<br>
 
<br>
 +
 +
==Translations==
 +
 +
* [http://zh.wikipedia.org/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8 &#20013;&#25991; : &#30495;&#20540;&#34920;]
    
==Syllabus==
 
==Syllabus==
 +
 +
===Focal nodes===
 +
 +
* [[Inquiry Live]]
 +
* [[Logic Live]]
 +
 +
===Peer nodes===
 +
 +
* [http://intersci.ss.uci.edu/wiki/index.php/Truth_table Truth Table @ InterSciWiki]
 +
* [http://mywikibiz.com/Truth_table Truth Table @ MyWikiBiz]
 +
* [http://ref.subwiki.org/wiki/Truth_table Truth Table @ Subject Wikis]
 +
* [http://en.wikiversity.org/wiki/Truth_table Truth Table @ Wikiversity]
 +
* [http://beta.wikiversity.org/wiki/Truth_table Truth Table @ Wikiversity Beta]
    
===Logical operators===
 
===Logical operators===
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{{col-break}}
 
{{col-break}}
 
* [[Ampheck]]
 
* [[Ampheck]]
* [[Boolean algebra]]
   
* [[Boolean domain]]
 
* [[Boolean domain]]
 
* [[Boolean function]]
 
* [[Boolean function]]
 +
* [[Boolean-valued function]]
 +
* [[Differential logic]]
 
{{col-break}}
 
{{col-break}}
* [[Boolean-valued function]]
  −
* [[Entitative graph]]
  −
* [[Existential graph]]
   
* [[Logical graph]]
 
* [[Logical graph]]
 +
* [[Minimal negation operator]]
 +
* [[Multigrade operator]]
 +
* [[Parametric operator]]
 +
* [[Peirce's law]]
 
{{col-break}}
 
{{col-break}}
* [[Minimal negation operator]]
  −
* [[Monadic predicate calculus]]
   
* [[Propositional calculus]]
 
* [[Propositional calculus]]
 +
* [[Sole sufficient operator]]
 +
* [[Truth table]]
 +
* [[Universe of discourse]]
 
* [[Zeroth order logic]]
 
* [[Zeroth order logic]]
 
{{col-end}}
 
{{col-end}}
   −
==Translations==
+
===Relational concepts===
 +
 
 +
{{col-begin}}
 +
{{col-break}}
 +
* [[Continuous predicate]]
 +
* [[Hypostatic abstraction]]
 +
* [[Logic of relatives]]
 +
* [[Logical matrix]]
 +
{{col-break}}
 +
* [[Relation (mathematics)|Relation]]
 +
* [[Relation composition]]
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* [[Relation construction]]
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* [[Relation reduction]]
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* [[Relation theory]]
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* [[Relative term]]
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* [[Sign relation]]
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* [[Triadic relation]]
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* [http://zh.wikipedia.org/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8 &#20013;&#25991; : &#30495;&#20540;&#34920;]
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===Information, Inquiry===
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==Document history==
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{{col-begin}}
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{{col-break}}
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]
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* [[Logic of information]]
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{{col-break}}
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* [[Descriptive science]]
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* [[Normative science]]
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{{col-break}}
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* [[Pragmatic maxim]]
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* [[Truth theory]]
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{{col-end}}
   −
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
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===Related articles===
    
{{col-begin}}
 
{{col-begin}}
 
{{col-break}}
 
{{col-break}}
* [http://mywikibiz.com/Truth_table Truth Table], [http://mywikibiz.com/ MyWikiBiz]
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
* [http://beta.wikiversity.org/wiki/Truth_table Truth Table], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
* [http://www.getwiki.net/-Truth_Table Truth Table], [http://www.getwiki.net/ GetWiki]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
 +
{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
 +
* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
 +
* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
 
{{col-break}}
 
{{col-break}}
* [http://www.wikinfo.org/index.php/Truth_table Truth Table], [http://www.wikinfo.org/ Wikinfo]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
* [http://www.textop.org/wiki/index.php?title=Truth_table Truth Table], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
* [http://en.wikipedia.org/w/index.php?title=Truth_table&oldid=77110085 Truth Table], [http://en.wikipedia.org/ Wikipedia]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 
{{col-end}}
 
{{col-end}}
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<br><sharethis />
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==Document history==
 +
 
 +
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
 +
 
 +
* [http://intersci.ss.uci.edu/wiki/index.php/Truth_table Truth Table], [http://intersci.ss.uci.edu/ InterSciWiki]
 +
* [http://mywikibiz.com/Truth_table Truth Table], [http://mywikibiz.com/ MyWikiBiz]
 +
* [http://semanticweb.org/wiki/Truth_table Truth Table], [http://semanticweb.org/ SemanticWeb]
 +
* [http://wikinfo.org/w/index.php/Truth_table Truth Table], [http://wikinfo.org/w/ Wikinfo]
 +
* [http://en.wikiversity.org/wiki/Truth_table Truth Table], [http://en.wikiversity.org/ Wikiversity]
 +
* [http://beta.wikiversity.org/wiki/Truth_table Truth Table], [http://beta.wikiversity.org/ Wikiversity Beta]
 +
* [http://en.wikipedia.org/w/index.php?title=Truth_table&oldid=77110085 Truth Table], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Inquiry]]
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[[Category:Open Educational Resource]]
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[[Category:Peer Educational Resource]]
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[[Category:Charles Sanders Peirce]]
 
[[Category:Combinatorics]]
 
[[Category:Combinatorics]]
 
[[Category:Computer Science]]
 
[[Category:Computer Science]]
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