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