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Lógica matemática/ Xv¬Y&¬Z<->X->¬Z

Expresión Xv¬Y&¬Z<->X->¬Z

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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