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