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