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