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