Truth table - Revision history

Jon Awbrey: update

2015-10-30T03:25:02Z

update

Jon Awbrey at 00:08, 30 October 2015

2015-10-30T00:08:15Z

Jon Awbrey: /* Peer nodes */ update

2012-05-16T15:14:11Z

Peer nodes: update

Jon Awbrey at 15:08, 16 May 2012

2012-05-16T15:08:15Z

Jon Awbrey: /* Logical NNOR */

2012-05-16T14:30:28Z

Logical NNOR

Jon Awbrey: /* Logical NAND */

2012-05-16T14:26:36Z

Logical NAND

Jon Awbrey: /* Logical implication */

2012-05-16T14:20:05Z

Logical implication

Jon Awbrey: /* Exclusive disjunction */

2012-05-16T13:58:20Z

Exclusive disjunction

Jon Awbrey: /* Logical equality */

2012-05-16T13:54:26Z

Logical equality

Jon Awbrey: /* Logical disjunction */

2012-05-16T13:52:16Z

Logical disjunction

@@ Line 254: / Line 254: @@
 ===Focal nodes===
 * [[Inquiry Live]]
 * [[Logic Live]]
 ===Peer nodes===
-{{col-begin}}
+* [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://beta.wikiversity.org/wiki/Truth_table Truth Table @ Wikiversity Beta]
 ===Logical operators===
@@ Line 351: / Line 342: @@
 ===Related articles===
-* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, &ldquo;Semiotic Information&rdquo;]
+{{col-begin}}
+{{col-break}}
-* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
+* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
+* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
-* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
+* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
+{{col-break}}
-* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
+* [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://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
+* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
+{{col-break}}
-* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
+* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
+* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
-* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
+* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
+{{col-end}}
 ==Document history==
@@ Line 371: / Line 361: @@
 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.
-{{col-begin}}
+* [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://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]
 [[Category:Inquiry]]

@@ Line 3: / Line 3: @@
 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 the lo<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.
+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==

@@ Line 266: / Line 266: @@
 {{col-break}}
 * [http://mywikibiz.com/Truth_table Truth Table @ MyWikiBiz]
-* [http://mathweb.org/wiki/Truth_table Truth Table @ MathWeb Wiki]
+* [http://intersci.ss.uci.edu/wiki/index.php/Truth_table Truth Table @ InterSciWiki]
 * [http://wiki.oercommons.org/mediawiki/index.php/Truth_table Truth Table @ OER Commons]
 {{col-break}}
 * [http://p2pfoundation.net/Truth_Table Truth Table @ P2P Foundation]
 * [http://ref.subwiki.org/wiki/Truth_table Truth Table @ Subject Wikis]
 * [http://beta.wikiversity.org/wiki/Truth_table Truth Table @ Wikiversity Beta]

@@ Line 389: / Line 389: @@
 * [http://en.wikipedia.org/w/index.php?title=Truth_table&oldid=77110085 Truth Table], [http://en.wikipedia.org/ Wikipedia]
 {{col-end}}
 [[Category:Inquiry]]

@@ Line 222: / Line 222: @@
 ==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>
-{| 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>
 |}

@@ Line 196: / Line 196: @@
 ==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>
-{| 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>
 |}

@@ Line 131: / Line 131: @@
 ==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>
-{| 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>
-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 \land q)
 \end{matrix}</math>
 ==Logical implication==