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