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