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