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