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