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