Sr Examen
Expresión ¬(¬(xy)∨(¬x¬y))xz∨xy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(x∧y)∨(x∧z∧(¬((¬(x∧y))∨((¬x)∧(¬y)))))
$$\left(x \wedge y\right) \vee \left(x \wedge z \wedge \neg \left(\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right)\right)\right)$$
Solución detallada
$$\neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\neg \left(\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right)\right) = x \wedge y$$
$$x \wedge z \wedge \neg \left(\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right)\right) = x \wedge y \wedge z$$
$$\left(x \wedge y\right) \vee \left(x \wedge z \wedge \neg \left(\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right)\right)\right) = x \wedge y$$
$$\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right) = \neg x \vee \neg y$$
$$\neg \left(\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right)\right) = x \wedge y$$
$$x \wedge z \wedge \neg \left(\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right)\right) = x \wedge y \wedge z$$
$$\left(x \wedge y\right) \vee \left(x \wedge z \wedge \neg \left(\left(\neg x \wedge \neg y\right) \vee \neg \left(x \wedge y\right)\right)\right) = x \wedge y$$
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 | 1 | +---+---+---+--------+