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