Expresión (x->y)(y->z)(z->u)

Ha introducido [src]

(x⇒y)∧(y⇒z)∧(z⇒u)

\left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right) \wedge \left(z \Rightarrow u\right)

Solución detallada

x \Rightarrow y = y \vee \neg x

y \Rightarrow z = z \vee \neg y

z \Rightarrow u = u \vee \neg z

\left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right) \wedge \left(z \Rightarrow u\right) = \left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)

Simplificación [src]

\left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)

(u∨(¬z))∧(y∨(¬x))∧(z∨(¬y))

Tabla de verdad

+---+---+---+---+--------+
| u | x | y | z | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+

FNC [src]

Ya está reducido a FNC

\left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)

(u∨(¬z))∧(y∨(¬x))∧(z∨(¬y))

FNCD [src]

\left(u \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg y\right)

(u∨(¬z))∧(y∨(¬x))∧(z∨(¬y))

FND [src]

\left(u \wedge y \wedge z\right) \vee \left(u \wedge y \wedge \neg y\right) \vee \left(u \wedge z \wedge \neg x\right) \vee \left(u \wedge \neg x \wedge \neg y\right) \vee \left(y \wedge z \wedge \neg z\right) \vee \left(y \wedge \neg y \wedge \neg z\right) \vee \left(z \wedge \neg x \wedge \neg z\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)

(u∧y∧z)∨(u∧y∧(¬y))∨(u∧z∧(¬x))∨(y∧z∧(¬z))∨(u∧(¬x)∧(¬y))∨(y∧(¬y)∧(¬z))∨(z∧(¬x)∧(¬z))∨((¬x)∧(¬y)∧(¬z))

FNDP [src]

\left(u \wedge y \wedge z\right) \vee \left(u \wedge \neg x \wedge \neg y\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)

(u∧y∧z)∨(u∧(¬x)∧(¬y))∨((¬x)∧(¬y)∧(¬z))

¿Cómo usar?

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