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Matematička logika: razlika između inačica

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m Članak "Matematička logika" je zaštićen: Zatrpavanje nedavnih promjena ([edit=autoconfirmed] (istječe 20:53, 19. prosinca 2011. (UTC)) [move=autoconfirmed] (istječe 20:53, 19. prosinca 2011. (UTC)))
Redak 387:
|align=center|ne
|-
|align=right|[[propositionalpropozicijska logiclogika]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">∧ <br/><br/>•<br/><br/>&</div>
||[[logicallogička conjunctionkonjunkcija]]
| rowspan=3|The statementIzraz ''A'' ∧ ''B'' isje trueistinit ifako su i ''A'' andi ''B'' are both trueistiniti; else ituostalom issu falseneistiniti.
| rowspan=3|''n''&nbsp;< 4&nbsp;&nbsp;∧&nbsp; ''n''&nbsp;>2&nbsp;&nbsp;⇔&nbsp; ''n''&nbsp;= 3 whenkada je ''n'' is a [[naturalprirodni numberbroj]].
! rowspan="3" |U+2227<br/><br/>U+0026
! rowspan="3" | &amp;and;<br/>&amp;amp;
! rowspan="3" | <math>\wedge</math>\wedge or \land<br/>\&<ref>Although this character is available in LaTeX, the [[Mediawiki]] TeX system doesn't support this character.</ref>
|-
|align=center|andi
|-
|align=right|[[propositionalpropozicijska logiclogika]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">∨<br/><br/>+<br/><br/>&#448;&#448;</div>
||[[logicallogička disjunctiondisjunkcija]]
| rowspan=3|The statementIzraz ''A'' ∨ ''B'' isje trueistinit ifako ''A'' orili ''B'' (orili bothoboje) aresu trueistiniti; ifako bothsu areoboje falseneistiniti, the statementizraz isje falseneistinit.
| rowspan=3|''n''&nbsp;≥ 4&nbsp;&nbsp;∨&nbsp; ''n''&nbsp;≤ 2&nbsp;&nbsp;⇔ ''n''&nbsp;≠ 3 whenkada je ''n'' is a [[naturalprirodni numberbroj]].
! rowspan="3" |U+2228
! rowspan="3" | &amp;or;
! rowspan="3" | <math>\lor</math>\lor or \vee
|-
|align=center|orili
|-
|align=right|[[propositionalpropozicijska logiclogika]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<br/><div style="font-size:200%;">⊕<br/><br/>{{Unicode|⊻}}</div> ||[[exclusive or|exclusiveizostavna disjunctiondisjunkcija]]
| rowspan=3| The statementIzraz ''A'' ⊕ ''B'' isje trueistinit whenkada eithersu bilo A orili B, butali notne bothoboje, are trueistiniti. ''A'' {{Unicode|⊻}} ''B'' means theznači sameisto.
| rowspan=3| (¬''A'') ⊕ ''A'' isje alwaysuvijek trueistinito, ''A'' ⊕ ''A'' isje alwaysuvijek falseneistinito.
! rowspan="3" |U+2295<br/><br/>U+22BB
! rowspan="3" | &amp;oplus;
Redak 422:
|align=center|xor
|-
|align=right|[[propositionalpropozicijska logiclogika]], [[Boolean algebra (logic)|BooleanIstina/neistina algebra]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<br/><div style="font-size:200%;">⊤<br/><br/>T<br/><br/>1</div> ||[[Tautology (logic)|TautologyTautologija]]
| rowspan=3| The statementIzraz ⊤ isje unconditionallybezuvjetno trueistinit.
| rowspan=3| ''A'' ⇒ ⊤ isje alwaysuvijek trueistinit.
! rowspan="3" |U+22A4
! rowspan="3" | T
! rowspan="3" | <math>\top</math>\top
|-
|align=center|topvrh
|-
|align=right|[[propositionalpropozicijska logiclogika]], [[Boolean algebra (logic)|Boolean algebra]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<br/><div style="font-size:200%;">⊥<br/><br/>F<br/><br/>0</div> ||[[ContradictionKontradikcija]]
| rowspan=3| The statementIzraz ⊥ isje unconditionallybezuvjetno falseneistinit.
| rowspan=3| ⊥ ⇒ ''A'' isje alwaysuvijek trueistinit.
! rowspan="3" |U+22A5
! rowspan="3" | &amp;perp;<br/>F
! rowspan="3" |<math>\bot</math>\bot
|-
|align=center|bottomdno
|-
|align=right|[[propositionalpropozicijska logiclogika]], [[Boolean algebra (logic)|Boolean algebra]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">∀</div>
||[[universaluniverzalna quantificationkvantifikacija]]
| rowspan=3|∀&nbsp;''x'': ''P''(''x'') meansznači da je ''P''(''x'') is trueistinit forza allsve ''x''.
| rowspan=3|∀&nbsp;''n''&nbsp;∈ '''N''': ''n''<sup>2</sup>&nbsp;≥ ''n''.
! rowspan="3" |U+2200
Redak 454:
! rowspan="3" | <math>\forall</math>\forall
|-
|align=center|forza allsve; forza anybilo što; forza eachsvaki
|-
|align=right|[[predicatepredikatna logiclogika]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">∃</div>
||[[egzistencijalna kvantifikacija]]
||[[existential quantification]]
| rowspan=3|∃&nbsp;''x'': ''P''(''x'') meansznači thereda ispostoji atbarem least onejedan ''x'' suchtakav thatda je ''P''(''x'') is trueistinit.
| rowspan=3|∃&nbsp;''n''&nbsp;∈ '''N''': ''n'' isje evenparan.
! rowspan="3" |U+2203
! rowspan="3" |&amp;exist;
! rowspan="3" | <math>\exists</math>\exists
|-
|align=center|there existspostoji
|-
|align=right|[[first-orderprvoredna logiclogika]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">∃!</div>
||[[kvantifikacija po posebnosti]]
||[[uniqueness quantification]]
| rowspan=3|∃!&nbsp;''x'': ''P''(''x'') meansznači thereda ispostoji exactlytočno onejedan ''x'' suchtakav thatda je ''P''(''x'') is trueistinit.
| rowspan=3|∃!&nbsp;''n''&nbsp;∈ '''N''': ''n''&nbsp;+ 5&nbsp;= 2''n''.
! rowspan="3" |U+2203&nbsp;U+0021
Redak 478:
! rowspan="3" |<math>\exists !</math>\exists !
|-
|align=center|therepostoji existstočno exactly onejedan
|-
|align=right|[[first-orderprvoredna logiclogika]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">:=<br/><br/>≡<br/><br/>:⇔</div>
||[[definitiondefinicija]]
| rowspan=3|''x''&nbsp;:= ''y'' or ''x''&nbsp;≡ ''y'' means ''x'' is defined to be another name for ''y'' (but note thatpazite: ≡ canmože alsoznačiti meani otherjoš thingsnešto, such aspoput [[congruence relation|congruencekongruencija]]).<br/><br/>''P''&nbsp;:⇔ ''Q'' means ''P'' is defined to be [[Logical equivalence|logicallylogički equivalentekvivalentni]] to ''Q''.
| rowspan=3|cosh&nbsp;''x''&nbsp;:= (1/2)(exp&nbsp;''x''&nbsp;+ exp&nbsp;(−''x''))<br/><br/>''A''&nbsp;XOR&nbsp;''B'' :⇔ (''A''&nbsp;∨&nbsp;''B'')&nbsp;∧&nbsp;¬(''A''&nbsp;∧&nbsp;''B'')
! rowspan="3" |U+2254 (U+003A&nbsp;U+003D)<br/><br/>U+2261<br/><br/>U+003A&nbsp;U+229C
Redak 490:
! rowspan="3" | <div><math>:=</math>:=<br/><math>\equiv</math>\equiv<br/><math>\Leftrightarrow</math>\Leftrightarrow</div>
|-
|align=center|isdefinirano defined askao
|-
|align=right|everywheresvugdje
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">( )</div>
||Precedentno grupiranje
||precedence grouping
| rowspan=3| PerformIzvodi theprvo operationsoperacije insideunutar the parentheses firstzagrada.
| rowspan=3|(8/4)/2&nbsp;= 2/2&nbsp;= 1, butali je 8/(4/2)&nbsp;= 8/2&nbsp;= 4.
! rowspan="3" |U+0028&nbsp;U+0029
! rowspan="3" | ( )
Redak 504:
|align=center|
|-
|align=right|everywheresvugdje
|-
| rowspan=3 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">{{Unicode|⊢}}</div>
||[[turnstileokretno]]
| rowspan=3|''x'' {{Unicode|⊢}} ''y'' meansznači da je ''y'' is provabledokazivo fromiz ''x'' (inu somenekon specifiedodređenom formalformalnom systemsistemu).
| rowspan=3| ''A'' → ''B'' {{Unicode|⊢}} ¬''B'' → ¬''A''
! rowspan="3" |U+22A6
Redak 514:
! rowspan="3" | <math>\vdash</math>\vdash
|-
|align=center|provabledokazivo
|-
|align=right|[[propositionalpropozicijska logiclogika]], [[first-orderprvoredna logiclogika]]
|-
| rowspan=3 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">&#8872;</div>
||[[doubledvostruki turnstilesmjer]]
| rowspan=3|''x'' &#8872; ''y'' meansznači da ''x'' semanticallysemantično entailsupotpunjuje ''y''
| rowspan=3| ''A'' → ''B'' &#8872; ¬''B'' → ¬''A''
! rowspan="3" |U+22A7
Redak 526:
! rowspan="3" | <math>\models</math>\models
|-
|align=center|entailsupotpunjuje
|-
|align=right|[[propositionalpropozicijska logiclogika]], [[first-orderprvoredna logiclogika]]
|}
Dobavljeno iz "https://hr.wikipedia.org/wiki/Matematička_logika"