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| [[File:Venn0100.svg||thumb|240px|[[Venn diagram]] of <math>A \nrightarrow B</math><br><br>[[File:Venn0101.svg|32px]] <math>\and</math> [[File:Venn1100.svg|32px]] <math>\Leftrightarrow</math> [[File:Venn0100.svg|40px]] <math>\Leftrightarrow \neg</math> [[File:Venn1011.svg|32px]] ]]
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| '''Material nonimplication''' or '''abjunction''' ([[latin]] ''ab'' = "from", ''junctio'' =–"joining") is the [[negation]] of [[Material conditional|material implication]]. That is to say that for any two [[proposition]]s P and Q, the material nonimplication from P to Q is true [[If and only if|if and only if]] P does not imply Q. | |
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| It may be written using logical notation as:
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| :: '''p⊅q'''
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| :: '''Lpq'''
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| :: '''p↛q'''
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| ==Definition==
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| ===Truth table===
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| {| border="1" cellpadding="1" cellspacing="0" style="text-align:center;"
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| |+
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| ! style="width:35px;background:#aaaaaa;" | p
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| ! style="width:35px;background:#aaaaaa;" | q
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| ! style="width:35px" | <math>~\nrightarrow</math>
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| |-
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| | T || T || F
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| |-
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| | T || F || T
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| |-
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| | F || T || F
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| |-
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| | F || F || F
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| |}
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| ==Properties==
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| '''falsehood-preserving''': The interpretation under which all variables are assigned a [[truth value]] of "false" produces a truth value of "false" as a result of material nonimplication.
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| ==Symbol==
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| The symbol for material nonimplication is simply a crossed-out material implication symbol. Its Unicode symbol is 8603 (decimal).
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| ==Natural language==
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| ===Grammatical===
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| ===Rhetorical===
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| "It's not the case that p implies q."<br />
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| "p but not q."
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| ===Colloquial===
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| "Just because p, doesn't mean q."
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| ==Boolean algebra==
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| {{Further|Boolean algebra}}
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| (A'+B)'
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| ==Computer science==
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| C: (A&(~B))
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| ==See also==
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| * [[Material conditional|Implication]]
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| == References ==
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| {{reflist}}
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| {{Logical connectives}}
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| [[Category:Logical connectives]]
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| {{mathlogic-stub}}
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| {{logic-stub}}
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Latest revision as of 21:19, 17 December 2014
The author's name is Christy. She is really fond of caving but she doesn't have the time lately. I've usually cherished residing in Alaska. My working day job is a travel agent.
Here is my web-site ... best psychic readings