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