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Lógica matemática/ not(z)<->not(x->(not(y)vz))

Expresión not(z)<->not(x->(not(y)vz))

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    Solución

    Ha introducido [src] 
    (¬z)⇔(¬(x⇒(z∨(¬y))))
    $$\neg z ⇔ x \not\Rightarrow \left(z \vee \neg y\right)$$
    Solución detallada
    $$x \Rightarrow \left(z \vee \neg y\right) = z \vee \neg x \vee \neg y$$
    $$x \not\Rightarrow \left(z \vee \neg y\right) = x \wedge y \wedge \neg z$$
    $$\neg z ⇔ x \not\Rightarrow \left(z \vee \neg y\right) = z \vee \left(x \wedge y\right)$$
    Simplificación [src]
    $$z \vee \left(x \wedge y\right)$$ 
    z∨(x∧y)
    Tabla de verdad 
    +---+---+---+--------+
| x | y | z | result |
+===+===+===+========+
| 0 | 0 | 0 | 0      |
+---+---+---+--------+
| 0 | 0 | 1 | 1      |
+---+---+---+--------+
| 0 | 1 | 0 | 0      |
+---+---+---+--------+
| 0 | 1 | 1 | 1      |
+---+---+---+--------+
| 1 | 0 | 0 | 0      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FND [src]
    Ya está reducido a FND
    $$z \vee \left(x \wedge y\right)$$ 
    z∨(x∧y)
    FNCD [src]
    $$\left(x \vee z\right) \wedge \left(y \vee z\right)$$ 
    (x∨z)∧(y∨z)
    FNC [src]
    $$\left(x \vee z\right) \wedge \left(y \vee z\right)$$ 
    (x∨z)∧(y∨z)
    FNDP [src]
    $$z \vee \left(x \wedge y\right)$$ 
    z∨(x∧y)
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