Sr Examen
Expresión —(x|z)|(y&—z)|—(x|—z)|(y&z)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
((¬(x|z))|(y∧(¬z)))|(((x)|z)|(y∧z))
$$\left(\neg \left(x | z\right) | \left(y \wedge \neg z\right)\right) | \left(\left(\left(x\right) | z\right) | \left(y \wedge z\right)\right)$$
Вы использовали:
| - Не-и (штрих Шеффера).
Возможно вы имели ввиду символ ∨ - Дизъюнкция (ИЛИ)?
Посмотреть с символом ∨
Solución detallada
$$x | z = \neg x \vee \neg z$$
$$\neg \left(x | z\right) = x \wedge z$$
$$\neg \left(x | z\right) | \left(y \wedge \neg z\right) = 1$$
$$x = \neg x$$
$$\left(x\right) | z = x \vee \neg z$$
$$\left(\left(x\right) | z\right) | \left(y \wedge z\right) = \neg x \vee \neg y \vee \neg z$$
$$\left(\neg \left(x | z\right) | \left(y \wedge \neg z\right)\right) | \left(\left(\left(x\right) | z\right) | \left(y \wedge z\right)\right) = x \wedge y \wedge z$$
$$\neg \left(x | z\right) = x \wedge z$$
$$\neg \left(x | z\right) | \left(y \wedge \neg z\right) = 1$$
$$x = \neg x$$
$$\left(x\right) | z = x \vee \neg z$$
$$\left(\left(x\right) | z\right) | \left(y \wedge z\right) = \neg x \vee \neg y \vee \neg z$$
$$\left(\neg \left(x | z\right) | \left(y \wedge \neg z\right)\right) | \left(\left(\left(x\right) | z\right) | \left(y \wedge z\right)\right) = x \wedge y \wedge z$$
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 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+