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