Sr Examen
Expresión ¬X3→(¬X1∨X2)*X3∨¬X1*X2→(X3∨X2)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬x3)⇒((x2∧(¬x1))∨(x3∧(x2∨(¬x1)))))⇒(x2∨x3)
$$\left(\neg x_{3} \Rightarrow \left(\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \left(x_{2} \vee \neg x_{1}\right)\right)\right)\right) \Rightarrow \left(x_{2} \vee x_{3}\right)$$
Solución detallada
$$\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \left(x_{2} \vee \neg x_{1}\right)\right) = \left(x_{2} \wedge x_{3}\right) \vee \left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1}\right)$$
$$\neg x_{3} \Rightarrow \left(\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \left(x_{2} \vee \neg x_{1}\right)\right)\right) = x_{3} \vee \left(x_{2} \wedge \neg x_{1}\right)$$
$$\left(\neg x_{3} \Rightarrow \left(\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \left(x_{2} \vee \neg x_{1}\right)\right)\right)\right) \Rightarrow \left(x_{2} \vee x_{3}\right) = 1$$
$$\neg x_{3} \Rightarrow \left(\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \left(x_{2} \vee \neg x_{1}\right)\right)\right) = x_{3} \vee \left(x_{2} \wedge \neg x_{1}\right)$$
$$\left(\neg x_{3} \Rightarrow \left(\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \left(x_{2} \vee \neg x_{1}\right)\right)\right)\right) \Rightarrow \left(x_{2} \vee x_{3}\right) = 1$$
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 | +----+----+----+--------+