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