Sr Examen
Expresión xyz∨x¬yz∨¬xy¬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∧y∧z)∨(x∧z∧(¬y))∨(y∧(¬x)∧(¬z)∧(x∨z∨(¬y))∧(y∨z∨(¬x))∧(x∨(¬y)∨(¬z)))
$$\left(x \wedge y \wedge z\right) \vee \left(x \wedge z \wedge \neg y\right) \vee \left(y \wedge \neg x \wedge \neg z \wedge \left(x \vee z \vee \neg y\right) \wedge \left(x \vee \neg y \vee \neg z\right) \wedge \left(y \vee z \vee \neg x\right)\right)$$
Solución detallada
$$y \wedge \neg x \wedge \neg z \wedge \left(x \vee z \vee \neg y\right) \wedge \left(x \vee \neg y \vee \neg z\right) \wedge \left(y \vee z \vee \neg x\right) = \text{False}$$
$$\left(x \wedge y \wedge z\right) \vee \left(x \wedge z \wedge \neg y\right) \vee \left(y \wedge \neg x \wedge \neg z \wedge \left(x \vee z \vee \neg y\right) \wedge \left(x \vee \neg y \vee \neg z\right) \wedge \left(y \vee z \vee \neg x\right)\right) = x \wedge z$$
$$\left(x \wedge y \wedge z\right) \vee \left(x \wedge z \wedge \neg y\right) \vee \left(y \wedge \neg x \wedge \neg z \wedge \left(x \vee z \vee \neg y\right) \wedge \left(x \vee \neg y \vee \neg z\right) \wedge \left(y \vee z \vee \neg x\right)\right) = x \wedge z$$
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 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+