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