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