Expresión ¬(¬X1¬X2⊕X3X4)X5
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\left(x_{3} \wedge x_{4}\right) ⊕ \left(\neg x_{1} \wedge \neg x_{2}\right) = \left(x_{3} \vee \neg x_{1}\right) \wedge \left(x_{3} \vee \neg x_{2}\right) \wedge \left(x_{4} \vee \neg x_{1}\right) \wedge \left(x_{4} \vee \neg x_{2}\right) \wedge \left(x_{1} \vee x_{2} \vee \neg x_{3} \vee \neg x_{4}\right)$$
$$\neg \left(\left(x_{3} \wedge x_{4}\right) ⊕ \left(\neg x_{1} \wedge \neg x_{2}\right)\right) = \left(x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1} \wedge \neg x_{2}\right)$$
$$x_{5} \wedge \neg \left(\left(x_{3} \wedge x_{4}\right) ⊕ \left(\neg x_{1} \wedge \neg x_{2}\right)\right) = x_{5} \wedge \left(x_{1} \vee x_{2} \vee x_{3}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{2} \vee \neg x_{3} \vee \neg x_{4}\right)$$
$$x_{5} \wedge \left(x_{1} \vee x_{2} \vee x_{3}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{2} \vee \neg x_{3} \vee \neg x_{4}\right)$$
x5∧(x1∨x2∨x3)∧(x1∨x2∨x4)∧((¬x1)∨(¬x3)∨(¬x4))∧((¬x2)∨(¬x3)∨(¬x4))
Tabla de verdad
+----+----+----+----+----+--------+
| x1 | x2 | x3 | x4 | x5 | result |
+====+====+====+====+====+========+
| 0 | 0 | 0 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 0 | 0 | 0 | 1 | 0 |
+----+----+----+----+----+--------+
| 0 | 0 | 0 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 0 | 0 | 1 | 1 | 0 |
+----+----+----+----+----+--------+
| 0 | 0 | 1 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 0 | 1 | 0 | 1 | 0 |
+----+----+----+----+----+--------+
| 0 | 0 | 1 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 0 | 1 | 1 | 1 | 1 |
+----+----+----+----+----+--------+
| 0 | 1 | 0 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 1 | 0 | 0 | 1 | 1 |
+----+----+----+----+----+--------+
| 0 | 1 | 0 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 1 | 0 | 1 | 1 | 1 |
+----+----+----+----+----+--------+
| 0 | 1 | 1 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 1 | 1 | 0 | 1 | 1 |
+----+----+----+----+----+--------+
| 0 | 1 | 1 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 0 | 1 | 1 | 1 | 1 | 0 |
+----+----+----+----+----+--------+
| 1 | 0 | 0 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 0 | 0 | 0 | 1 | 1 |
+----+----+----+----+----+--------+
| 1 | 0 | 0 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 0 | 0 | 1 | 1 | 1 |
+----+----+----+----+----+--------+
| 1 | 0 | 1 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 0 | 1 | 0 | 1 | 1 |
+----+----+----+----+----+--------+
| 1 | 0 | 1 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 0 | 1 | 1 | 1 | 0 |
+----+----+----+----+----+--------+
| 1 | 1 | 0 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 1 | 0 | 0 | 1 | 1 |
+----+----+----+----+----+--------+
| 1 | 1 | 0 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 1 | 0 | 1 | 1 | 1 |
+----+----+----+----+----+--------+
| 1 | 1 | 1 | 0 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 1 | 1 | 0 | 1 | 1 |
+----+----+----+----+----+--------+
| 1 | 1 | 1 | 1 | 0 | 0 |
+----+----+----+----+----+--------+
| 1 | 1 | 1 | 1 | 1 | 0 |
+----+----+----+----+----+--------+
$$\left(x_{1} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right)$$
(x1∧x5∧(¬x3))∨(x1∧x5∧(¬x4))∨(x2∧x5∧(¬x3))∨(x2∧x5∧(¬x4))∨(x3∧x4∧x5∧(¬x1)∧(¬x2))
$$\left(x_{1} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right)$$
(x1∧x5∧(¬x3))∨(x1∧x5∧(¬x4))∨(x2∧x5∧(¬x3))∨(x2∧x5∧(¬x4))∨(x1∧x2∧x5∧(¬x3))∨(x1∧x2∧x5∧(¬x4))∨(x1∧x3∧x5∧(¬x3))∨(x1∧x3∧x5∧(¬x4))∨(x1∧x4∧x5∧(¬x3))∨(x1∧x4∧x5∧(¬x4))∨(x2∧x3∧x5∧(¬x3))∨(x2∧x3∧x5∧(¬x4))∨(x2∧x4∧x5∧(¬x3))∨(x2∧x4∧x5∧(¬x4))∨(x3∧x4∧x5∧(¬x3))∨(x3∧x4∧x5∧(¬x4))∨(x1∧x5∧(¬x1)∧(¬x2))∨(x1∧x5∧(¬x1)∧(¬x3))∨(x1∧x5∧(¬x1)∧(¬x4))∨(x1∧x5∧(¬x2)∧(¬x3))∨(x1∧x5∧(¬x2)∧(¬x4))∨(x1∧x5∧(¬x3)∧(¬x4))∨(x2∧x5∧(¬x1)∧(¬x2))∨(x2∧x5∧(¬x1)∧(¬x3))∨(x2∧x5∧(¬x1)∧(¬x4))∨(x2∧x5∧(¬x2)∧(¬x3))∨(x2∧x5∧(¬x2)∧(¬x4))∨(x2∧x5∧(¬x3)∧(¬x4))∨(x1∧x2∧x5∧(¬x1)∧(¬x2))∨(x1∧x2∧x5∧(¬x1)∧(¬x3))∨(x1∧x2∧x5∧(¬x1)∧(¬x4))∨(x1∧x2∧x5∧(¬x2)∧(¬x3))∨(x1∧x2∧x5∧(¬x2)∧(¬x4))∨(x1∧x2∧x5∧(¬x3)∧(¬x4))∨(x1∧x3∧x5∧(¬x1)∧(¬x2))∨(x1∧x3∧x5∧(¬x1)∧(¬x3))∨(x1∧x3∧x5∧(¬x1)∧(¬x4))∨(x1∧x3∧x5∧(¬x2)∧(¬x3))∨(x1∧x3∧x5∧(¬x2)∧(¬x4))∨(x1∧x3∧x5∧(¬x3)∧(¬x4))∨(x1∧x4∧x5∧(¬x1)∧(¬x2))∨(x1∧x4∧x5∧(¬x1)∧(¬x3))∨(x1∧x4∧x5∧(¬x1)∧(¬x4))∨(x1∧x4∧x5∧(¬x2)∧(¬x3))∨(x1∧x4∧x5∧(¬x2)∧(¬x4))∨(x1∧x4∧x5∧(¬x3)∧(¬x4))∨(x2∧x3∧x5∧(¬x1)∧(¬x2))∨(x2∧x3∧x5∧(¬x1)∧(¬x3))∨(x2∧x3∧x5∧(¬x1)∧(¬x4))∨(x2∧x3∧x5∧(¬x2)∧(¬x3))∨(x2∧x3∧x5∧(¬x2)∧(¬x4))∨(x2∧x3∧x5∧(¬x3)∧(¬x4))∨(x2∧x4∧x5∧(¬x1)∧(¬x2))∨(x2∧x4∧x5∧(¬x1)∧(¬x3))∨(x2∧x4∧x5∧(¬x1)∧(¬x4))∨(x2∧x4∧x5∧(¬x2)∧(¬x3))∨(x2∧x4∧x5∧(¬x2)∧(¬x4))∨(x2∧x4∧x5∧(¬x3)∧(¬x4))∨(x3∧x4∧x5∧(¬x1)∧(¬x2))∨(x3∧x4∧x5∧(¬x1)∧(¬x3))∨(x3∧x4∧x5∧(¬x1)∧(¬x4))∨(x3∧x4∧x5∧(¬x2)∧(¬x3))∨(x3∧x4∧x5∧(¬x2)∧(¬x4))∨(x3∧x4∧x5∧(¬x3)∧(¬x4))
Ya está reducido a FNC
$$x_{5} \wedge \left(x_{1} \vee x_{2} \vee x_{3}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{2} \vee \neg x_{3} \vee \neg x_{4}\right)$$
x5∧(x1∨x2∨x3)∧(x1∨x2∨x4)∧((¬x1)∨(¬x3)∨(¬x4))∧((¬x2)∨(¬x3)∨(¬x4))
$$x_{5} \wedge \left(x_{1} \vee x_{2} \vee x_{3}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{2} \vee \neg x_{3} \vee \neg x_{4}\right)$$
x5∧(x1∨x2∨x3)∧(x1∨x2∨x4)∧((¬x1)∨(¬x3)∨(¬x4))∧((¬x2)∨(¬x3)∨(¬x4))