Sr Examen
Expresión ¬((xvy&z)(¬xv¬y))&xvy&¬z
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(y∧(¬z))∨(x∧(¬((x∨(y∧z))∧((¬x)∨(¬y)))))
$$\left(x \wedge \neg \left(\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right)\right)\right) \vee \left(y \wedge \neg z\right)$$
Solución detallada
$$\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right) = \left(x \vee y\right) \wedge \left(x \vee z\right) \wedge \left(\neg x \vee \neg y\right)$$
$$\neg \left(\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right)\right) = \left(x \wedge y\right) \vee \left(\neg x \wedge \neg y\right) \vee \left(\neg x \wedge \neg z\right)$$
$$x \wedge \neg \left(\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right)\right) = x \wedge y$$
$$\left(x \wedge \neg \left(\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right)\right)\right) \vee \left(y \wedge \neg z\right) = y \wedge \left(x \vee \neg z\right)$$
$$\neg \left(\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right)\right) = \left(x \wedge y\right) \vee \left(\neg x \wedge \neg y\right) \vee \left(\neg x \wedge \neg z\right)$$
$$x \wedge \neg \left(\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right)\right) = x \wedge y$$
$$\left(x \wedge \neg \left(\left(x \vee \left(y \wedge z\right)\right) \wedge \left(\neg x \vee \neg y\right)\right)\right) \vee \left(y \wedge \neg z\right) = y \wedge \left(x \vee \neg z\right)$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+