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