Sr Examen
Expresión (xy∨xyz)&(¬(xy)∨¬(xyz))
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Solución
Ha introducido
[src]
((x∧y)∨(x∧y∧z))∧((¬(x∧y))∨(¬(x∧y∧z)))
$$\left(\left(x \wedge y\right) \vee \left(x \wedge y \wedge z\right)\right) \wedge \left(\neg \left(x \wedge y\right) \vee \neg \left(x \wedge y \wedge z\right)\right)$$
Solución detallada
$$\left(x \wedge y\right) \vee \left(x \wedge y \wedge z\right) = x \wedge y$$
$$\neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\neg \left(x \wedge y \wedge z\right) = \neg x \vee \neg y \vee \neg z$$
$$\neg \left(x \wedge y\right) \vee \neg \left(x \wedge y \wedge z\right) = \neg x \vee \neg y \vee \neg z$$
$$\left(\left(x \wedge y\right) \vee \left(x \wedge y \wedge z\right)\right) \wedge \left(\neg \left(x \wedge y\right) \vee \neg \left(x \wedge y \wedge z\right)\right) = x \wedge y \wedge \neg z$$
$$\neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\neg \left(x \wedge y \wedge z\right) = \neg x \vee \neg y \vee \neg z$$
$$\neg \left(x \wedge y\right) \vee \neg \left(x \wedge y \wedge z\right) = \neg x \vee \neg y \vee \neg z$$
$$\left(\left(x \wedge y\right) \vee \left(x \wedge y \wedge z\right)\right) \wedge \left(\neg \left(x \wedge y\right) \vee \neg \left(x \wedge y \wedge z\right)\right) = x \wedge y \wedge \neg z$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+