Sr Examen
Lógica matemática/ ¬x¬y¬z¬t+¬x¬yz¬t+¬xy¬z¬t+¬xy¬zt+¬xyz¬t+x¬yzt+xy¬z¬t+xy¬zt+xy¬zt+xyz¬t+xyzt

Expresión ¬x¬y¬z¬t+¬x¬yz¬t+¬xy¬z¬t+¬xy¬zt+¬xyz¬t+x¬yzt+xy¬z¬t+xy¬zt+xy¬zt+xyz¬t+xyzt

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (t∧x∧y∧z)∨(t∧x∧y∧(¬z))∨(t∧x∧z∧(¬y))∨(x∧y∧z∧(¬t))∨(t∧y∧(¬x)∧(¬z))∨(x∧y∧(¬t)∧(¬z))∨(y∧z∧(¬t)∧(¬x))∨(y∧(¬t)∧(¬x)∧(¬z))∨(z∧(¬t)∧(¬x)∧(¬y))∨((¬t)∧(¬x)∧(¬y)∧(¬z))
    $$\left(t \wedge x \wedge y \wedge z\right) \vee \left(t \wedge x \wedge y \wedge \neg z\right) \vee \left(t \wedge x \wedge z \wedge \neg y\right) \vee \left(t \wedge y \wedge \neg x \wedge \neg z\right) \vee \left(x \wedge y \wedge z \wedge \neg t\right) \vee \left(x \wedge y \wedge \neg t \wedge \neg z\right) \vee \left(y \wedge z \wedge \neg t \wedge \neg x\right) \vee \left(y \wedge \neg t \wedge \neg x \wedge \neg z\right) \vee \left(z \wedge \neg t \wedge \neg x \wedge \neg y\right) \vee \left(\neg t \wedge \neg x \wedge \neg y \wedge \neg z\right)$$
    Solución detallada
    $$\left(t \wedge x \wedge y \wedge z\right) \vee \left(t \wedge x \wedge y \wedge \neg z\right) \vee \left(t \wedge x \wedge z \wedge \neg y\right) \vee \left(t \wedge y \wedge \neg x \wedge \neg z\right) \vee \left(x \wedge y \wedge z \wedge \neg t\right) \vee \left(x \wedge y \wedge \neg t \wedge \neg z\right) \vee \left(y \wedge z \wedge \neg t \wedge \neg x\right) \vee \left(y \wedge \neg t \wedge \neg x \wedge \neg z\right) \vee \left(z \wedge \neg t \wedge \neg x \wedge \neg y\right) \vee \left(\neg t \wedge \neg x \wedge \neg y \wedge \neg z\right) = \left(y \wedge \neg t\right) \vee \left(y \wedge \neg z\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(t \wedge x \wedge z\right)$$
    Simplificación [src]
    $$\left(y \wedge \neg t\right) \vee \left(y \wedge \neg z\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(t \wedge x \wedge z\right)$$ 
    (y∧(¬t))∨(y∧(¬z))∨(t∧x∧z)∨((¬t)∧(¬x))
    Tabla de verdad 
    +---+---+---+---+--------+
| t | x | y | z | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNDP [src]
    $$\left(y \wedge \neg t\right) \vee \left(y \wedge \neg z\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(t \wedge x \wedge z\right)$$ 
    (y∧(¬t))∨(y∧(¬z))∨(t∧x∧z)∨((¬t)∧(¬x))
    FNC [src]
    $$\left(t \vee y \vee \neg t\right) \wedge \left(t \vee y \vee \neg x\right) \wedge \left(t \vee \neg t \vee \neg z\right) \wedge \left(x \vee y \vee \neg t\right) \wedge \left(x \vee y \vee \neg x\right) \wedge \left(x \vee \neg t \vee \neg z\right) \wedge \left(y \vee z \vee \neg t\right) \wedge \left(y \vee z \vee \neg x\right) \wedge \left(z \vee \neg t \vee \neg z\right) \wedge \left(t \vee y \vee \neg t \vee \neg x\right) \wedge \left(t \vee y \vee \neg t \vee \neg z\right) \wedge \left(t \vee y \vee \neg x \vee \neg z\right) \wedge \left(t \vee \neg t \vee \neg x \vee \neg z\right) \wedge \left(x \vee y \vee \neg t \vee \neg x\right) \wedge \left(x \vee y \vee \neg t \vee \neg z\right) \wedge \left(x \vee y \vee \neg x \vee \neg z\right) \wedge \left(x \vee \neg t \vee \neg x \vee \neg z\right) \wedge \left(y \vee z \vee \neg t \vee \neg x\right) \wedge \left(y \vee z \vee \neg t \vee \neg z\right) \wedge \left(y \vee z \vee \neg x \vee \neg z\right) \wedge \left(z \vee \neg t \vee \neg x \vee \neg z\right)$$ 
    (t∨y∨(¬t))∧(t∨y∨(¬x))∧(x∨y∨(¬t))∧(x∨y∨(¬x))∧(y∨z∨(¬t))∧(y∨z∨(¬x))∧(t∨(¬t)∨(¬z))∧(x∨(¬t)∨(¬z))∧(z∨(¬t)∨(¬z))∧(t∨y∨(¬t)∨(¬x))∧(t∨y∨(¬t)∨(¬z))∧(t∨y∨(¬x)∨(¬z))∧(x∨y∨(¬t)∨(¬x))∧(x∨y∨(¬t)∨(¬z))∧(x∨y∨(¬x)∨(¬z))∧(y∨z∨(¬t)∨(¬x))∧(y∨z∨(¬t)∨(¬z))∧(y∨z∨(¬x)∨(¬z))∧(t∨(¬t)∨(¬x)∨(¬z))∧(x∨(¬t)∨(¬x)∨(¬z))∧(z∨(¬t)∨(¬x)∨(¬z))
    FND [src]
    Ya está reducido a FND
    $$\left(y \wedge \neg t\right) \vee \left(y \wedge \neg z\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(t \wedge x \wedge z\right)$$ 
    (y∧(¬t))∨(y∧(¬z))∨(t∧x∧z)∨((¬t)∧(¬x))
    FNCD [src]
    $$\left(t \vee y \vee \neg x\right) \wedge \left(x \vee \neg t \vee \neg z\right) \wedge \left(y \vee z \vee \neg t\right)$$ 
    (t∨y∨(¬x))∧(y∨z∨(¬t))∧(x∨(¬t)∨(¬z))
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