Sr Examen
Expresión не(не(x1+не(x2*неx3))*x3*неx4)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
¬(x3∧(¬x4)∧(¬(x1∨(¬(x2∧(¬x3))))))
$$\neg \left(x_{3} \wedge \neg x_{4} \wedge \neg \left(x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right)\right)\right)$$
Solución detallada
$$\neg \left(x_{2} \wedge \neg x_{3}\right) = x_{3} \vee \neg x_{2}$$
$$x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right) = x_{1} \vee x_{3} \vee \neg x_{2}$$
$$\neg \left(x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right)\right) = x_{2} \wedge \neg x_{1} \wedge \neg x_{3}$$
$$x_{3} \wedge \neg x_{4} \wedge \neg \left(x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right)\right) = \text{False}$$
$$\neg \left(x_{3} \wedge \neg x_{4} \wedge \neg \left(x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right)\right)\right) = 1$$
$$x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right) = x_{1} \vee x_{3} \vee \neg x_{2}$$
$$\neg \left(x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right)\right) = x_{2} \wedge \neg x_{1} \wedge \neg x_{3}$$
$$x_{3} \wedge \neg x_{4} \wedge \neg \left(x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right)\right) = \text{False}$$
$$\neg \left(x_{3} \wedge \neg x_{4} \wedge \neg \left(x_{1} \vee \neg \left(x_{2} \wedge \neg x_{3}\right)\right)\right) = 1$$
Tabla de verdad
+----+----+----+----+--------+ | x1 | x2 | x3 | x4 | result | +====+====+====+====+========+ | 0 | 0 | 0 | 0 | 1 | +----+----+----+----+--------+ | 0 | 0 | 0 | 1 | 1 | +----+----+----+----+--------+ | 0 | 0 | 1 | 0 | 1 | +----+----+----+----+--------+ | 0 | 0 | 1 | 1 | 1 | +----+----+----+----+--------+ | 0 | 1 | 0 | 0 | 1 | +----+----+----+----+--------+ | 0 | 1 | 0 | 1 | 1 | +----+----+----+----+--------+ | 0 | 1 | 1 | 0 | 1 | +----+----+----+----+--------+ | 0 | 1 | 1 | 1 | 1 | +----+----+----+----+--------+ | 1 | 0 | 0 | 0 | 1 | +----+----+----+----+--------+ | 1 | 0 | 0 | 1 | 1 | +----+----+----+----+--------+ | 1 | 0 | 1 | 0 | 1 | +----+----+----+----+--------+ | 1 | 0 | 1 | 1 | 1 | +----+----+----+----+--------+ | 1 | 1 | 0 | 0 | 1 | +----+----+----+----+--------+ | 1 | 1 | 0 | 1 | 1 | +----+----+----+----+--------+ | 1 | 1 | 1 | 0 | 1 | +----+----+----+----+--------+ | 1 | 1 | 1 | 1 | 1 | +----+----+----+----+--------+