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