Sr Examen
Lógica matemática/ ¬x¬y¬t+¬xyt+yz+x¬y+xy¬z

Expresión ¬x¬y¬t+¬xyt+yz+x¬y+xy¬z

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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