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