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

Expresión not(x)or(((y->z)andx)or(y<->z))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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