Sr Examen
Expresión (xy+(y¬z∨xz))z∨¬x¬y¬z
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬x)∧(¬y)∧(¬z))∨(z∧((x∧y)∨(x∧z)∨(y∧(¬z))))
$$\left(z \wedge \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge \neg z\right)\right)\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)$$
Solución detallada
$$\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge \neg z\right) = \left(x \wedge z\right) \vee \left(y \wedge \neg z\right)$$
$$z \wedge \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge \neg z\right)\right) = x \wedge z$$
$$\left(z \wedge \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge \neg z\right)\right)\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right) = \left(x \vee \neg z\right) \wedge \left(z \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
$$z \wedge \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge \neg z\right)\right) = x \wedge z$$
$$\left(z \wedge \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge \neg z\right)\right)\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right) = \left(x \vee \neg z\right) \wedge \left(z \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
Simplificación
[src]
$$\left(x \vee \neg z\right) \wedge \left(z \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
(x∨(¬z))∧(z∨(¬x))∧(z∨(¬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 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNDP
[src]
$$\left(x \wedge z\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)$$
(x∧z)∨((¬x)∧(¬y)∧(¬z))
FND
[src]
$$\left(x \wedge z\right) \vee \left(z \wedge \neg z\right) \vee \left(x \wedge z \wedge \neg x\right) \vee \left(x \wedge z \wedge \neg y\right) \vee \left(x \wedge \neg x \wedge \neg y\right) \vee \left(z \wedge \neg x \wedge \neg z\right) \vee \left(z \wedge \neg y \wedge \neg z\right) \vee \left(\neg x \wedge \neg y \wedge \neg z\right)$$
(x∧z)∨(z∧(¬z))∨(x∧z∧(¬x))∨(x∧z∧(¬y))∨(x∧(¬x)∧(¬y))∨(z∧(¬x)∧(¬z))∨(z∧(¬y)∧(¬z))∨((¬x)∧(¬y)∧(¬z))
FNC
[src]
Ya está reducido a FNC
$$\left(x \vee \neg z\right) \wedge \left(z \vee \neg x\right) \wedge \left(z \vee \neg y\right)$$
(x∨(¬z))∧(z∨(¬x))∧(z∨(¬y))
FNCD
[src]
$$\left(x \vee \neg y\right) \wedge \left(x \vee \neg z\right) \wedge \left(z \vee \neg x\right)$$
(x∨(¬y))∧(x∨(¬z))∧(z∨(¬x))