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