Difference between revisions of "Exercícios de Dedução Natural"

Revision as of 12:31, 14 September 2020

$\varphi \land \psi \vdash \psi \land \varphi$
$(\varphi \land \psi )\land \delta \vdash \varphi \land (\psi \land \delta )$
$\varphi \vdash \varphi \land \varphi$
$\alpha \land \beta ,\gamma \land \delta \vdash \gamma \land \beta$
$\alpha \to (\beta \to \gamma )\vdash \beta \to (\alpha \to \gamma )$
$\vdash \alpha \to (\beta \to \alpha )$
$\vdash \alpha \to \alpha$
$\alpha \to \beta \vdash \alpha \to (\alpha \to \beta )$
$\alpha \to (\alpha \to \beta )\vdash \alpha \to \beta$
$\gamma \to \alpha ,\gamma \to \beta \vdash \gamma \to (\alpha \land \beta )$
$\beta \lor (\alpha \land \beta )\vdash \beta$
$(\alpha \lor \beta )\to \gamma \vdash (\alpha \to \gamma )\land (\beta \to \gamma )$
$\alpha \lor \beta \not \vdash \alpha \land \beta$

Terceiro Excluído / Tertium Non Datur: $\vdash \varphi \lor \neg \varphi$
Tarefa: Demonstrar a mesma fórmula, invertendo a ordem de aplicação das regras de introdução da disjunção.

@@ Line 21: / Line 21: @@
 #<math>\gamma \to \alpha, \gamma \to \beta \vdash \gamma \to (\alpha \land \beta)</math><!--
 --><p>{{#ev:youtube|mlEYLd56pMg|||||start=1098}}</p>
+<!---->
 #<math>\beta \lor (\alpha \land \beta) \vdash \beta</math><!--
 --><p>{{#ev:youtube|yUejpYb2NgI|||||start=759}}</p>
@@ Line 27: / Line 27: @@
 --><p>{{#ev:youtube|yUejpYb2NgI|||||start=850}}</p>
 #<math>\alpha \lor \beta \not\vdash \alpha \land \beta</math><!--
---><p>{{#ev:youtube|yUejpYb2NgI|||||start=1424}}</p>
+--><p>{{#ev:youtube|yUejpYb2NgI|||||start=1231}}</p>
 ==Dedução Natural para a Lógica Proposicional Clássica==