Expresión ((P∧¬Q)→(¬Q∧R))∧(R→¬P)
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$r \Rightarrow \neg p = \neg p \vee \neg r$$
$$\left(p \wedge \neg q\right) \Rightarrow \left(r \wedge \neg q\right) = q \vee r \vee \neg p$$
$$\left(r \Rightarrow \neg p\right) \wedge \left(\left(p \wedge \neg q\right) \Rightarrow \left(r \wedge \neg q\right)\right) = \left(q \wedge \neg r\right) \vee \neg p$$
$$\left(q \wedge \neg r\right) \vee \neg p$$
Tabla de verdad
+---+---+---+--------+
| p | q | r | result |
+===+===+===+========+
| 0 | 0 | 0 | 1 |
+---+---+---+--------+
| 0 | 0 | 1 | 1 |
+---+---+---+--------+
| 0 | 1 | 0 | 1 |
+---+---+---+--------+
| 0 | 1 | 1 | 1 |
+---+---+---+--------+
| 1 | 0 | 0 | 0 |
+---+---+---+--------+
| 1 | 0 | 1 | 0 |
+---+---+---+--------+
| 1 | 1 | 0 | 1 |
+---+---+---+--------+
| 1 | 1 | 1 | 0 |
+---+---+---+--------+
$$\left(q \wedge \neg r\right) \vee \neg p$$
$$\left(q \vee \neg p\right) \wedge \left(\neg p \vee \neg r\right)$$
$$\left(q \vee \neg p\right) \wedge \left(\neg p \vee \neg r\right)$$
Ya está reducido a FND
$$\left(q \wedge \neg r\right) \vee \neg p$$