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Lógica matemática/ x*not(z)+not(x)*y*z+not(x)*not(y)*not(z)

Expresión x*not(z)+not(x)*y*z+not(x)*not(y)*not(z)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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