« Logique (mathématiques)/Exercices/Forme Normale Disjonctive » : différence entre les versions

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Ligne 15 :
# Conserver les contextes de cette table où <math>\phi = 1</math>
 
=== {{Solution ===
| contenu =
{|{{!}} class="wikitable"
! <math>x</math>
{{!}} <math>yx</math>
{{!}} <math>zy</math>
{{!}} <math>\neg (x \and y \and z)</math>
{{!}} <math>\neg (x \and y \and z)</math>
{{!}} <math>x \and zy</math>
{{!}} <math>yx \and z</math>
{{!}} <math>y \phiand z</math>
{{!}} <math>x\phi</math>
|{{!}}-----
| 0
|{{!}} 0
|{{!}} 0
{{!}} 0
| 1
{{!}} 1
| 0
|{{!}} 0
|{{!}} 0
|{{!}} 0
{{!}} 0
|-
{{!}}-
| 0
|{{!}} 0
{{!}} 0
| 1
|{{!}} 1
{{!}} 1
| 0
|{{!}} 0
|{{!}} 0
|{{!}} 0
{{!}} 0
|{{!}}-----
| 0
{{!}} 0
| 1
{{!}} 1
| 0
{{!}} 0
| 1
{{!}} 1
| 0
|{{!}} 0
|{{!}} 0
|{{!}} 0
{{!}} 0
|-
{{!}}-
| 0
{{!}} 0
| 1
|{{!}} 1
|{{!}} 1
{{!}} 1
| 0
|{{!}} 0
{{!}} 0
| 1
|{{!}} 1
{{!}} 1
|{{!}}-----
| 1
{{!}} 1
| 0
|{{!}} 0
{{!}} 0
| 1
{{!}} 1
| 0
|{{!}} 0
|{{!}} 0
|{{!}} 0
{{!}} 0
|-
{{!}}-
| 1
{{!}} 1
| 0
{{!}} 0
| 1
|{{!}} 1
{{!}} 1
| 0
{{!}} 0
| 1
{{!}} 1
| 0
{{!}} 0
| 1
{{!}} 1
|{{!}}-----
| 1
|{{!}} 1
{{!}} 1
| 0
{{!}} 0
| 1
|{{!}} 1
{{!}} 1
| 0
|{{!}} 0
{{!}} 0
| 1
{{!}} 1
|-
{{!}}-
| 1
|{{!}} 1
|{{!}} 1
{{!}} 1
| 0
{{!}} 0
| 1
|{{!}} 1
|{{!}} 1
{{!}} 1
| 0
{{!}} 0
|}
{{!}}}
 
 
La FND de <math>\phi</math> est <math>(\neg x \and y \and z) \or (x \and \neg y \and z) \or (x \and y \and \neg z)</math>
|}}
 
 
=== Partie B ===
Ligne 110 ⟶ 111 :
# Conserver les contextes de cette table où <math>\psi = 1</math>
 
=== {{Solution ===
| contenu =
{| class="wikitable"
! <math>x</math>
Ligne 177 ⟶ 179 :
 
La FND de <math>\psi</math> est <math>(\neg x \and \neg y \and z) \or (\neg x \and y \and \neg z) \or (\neg x \and y \and z) \or (x \and \neg y \and \neg z) \or (x \and \neg y \and z) \or (x \and y \and \neg z)</math>
}}
 
=== Partie C ===