Sr Examen
Expresión ¬(x2&x1⊕x3∨¬x1⊕x3&x1)⊕(x2∨¬x1)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(x2∨(¬x1))⊕(¬((x1∧x2)⊕(x1∧x3)⊕(x3∨(¬x1))))
$$\left(x_{2} \vee \neg x_{1}\right) ⊕ \neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right)$$
Solución detallada
$$\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right) = x_{2} \vee \neg x_{1}$$
$$\neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right) = x_{1} \wedge \neg x_{2}$$
$$\left(x_{2} \vee \neg x_{1}\right) ⊕ \neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right) = 1$$
$$\neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right) = x_{1} \wedge \neg x_{2}$$
$$\left(x_{2} \vee \neg x_{1}\right) ⊕ \neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right) = 1$$
Tabla de verdad
+----+----+----+--------+ | x1 | x2 | x3 | result | +====+====+====+========+ | 0 | 0 | 0 | 1 | +----+----+----+--------+ | 0 | 0 | 1 | 1 | +----+----+----+--------+ | 0 | 1 | 0 | 1 | +----+----+----+--------+ | 0 | 1 | 1 | 1 | +----+----+----+--------+ | 1 | 0 | 0 | 1 | +----+----+----+--------+ | 1 | 0 | 1 | 1 | +----+----+----+--------+ | 1 | 1 | 0 | 1 | +----+----+----+--------+ | 1 | 1 | 1 | 1 | +----+----+----+--------+