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
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \left(c \wedge \neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right) = \left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
$$\left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
(a∧b∧c)∨((¬a)∧(¬b))∨((¬b)∧(¬c))
Tabla de verdad
+---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 1 |
+---+---+---+--------+
| 0 | 0 | 1 | 1 |
+---+---+---+--------+
| 0 | 1 | 0 | 0 |
+---+---+---+--------+
| 0 | 1 | 1 | 0 |
+---+---+---+--------+
| 1 | 0 | 0 | 1 |
+---+---+---+--------+
| 1 | 0 | 1 | 0 |
+---+---+---+--------+
| 1 | 1 | 0 | 0 |
+---+---+---+--------+
| 1 | 1 | 1 | 1 |
+---+---+---+--------+
$$\left(a \vee \neg b\right) \wedge \left(c \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg c\right)$$
(a∨(¬b))∧(c∨(¬b))∧(b∨(¬a)∨(¬c))
$$\left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
(a∧b∧c)∨((¬a)∧(¬b))∨((¬b)∧(¬c))
$$\left(a \vee \neg b\right) \wedge \left(b \vee \neg b\right) \wedge \left(c \vee \neg b\right) \wedge \left(a \vee \neg a \vee \neg b\right) \wedge \left(a \vee \neg a \vee \neg c\right) \wedge \left(a \vee \neg b \vee \neg c\right) \wedge \left(b \vee \neg a \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg c\right) \wedge \left(b \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg b \vee \neg c\right)$$
(a∨(¬b))∧(b∨(¬b))∧(c∨(¬b))∧(a∨(¬a)∨(¬b))∧(a∨(¬a)∨(¬c))∧(a∨(¬b)∨(¬c))∧(b∨(¬a)∨(¬b))∧(b∨(¬a)∨(¬c))∧(b∨(¬b)∨(¬c))∧(c∨(¬a)∨(¬b))∧(c∨(¬a)∨(¬c))∧(c∨(¬b)∨(¬c))
Ya está reducido a FND
$$\left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
(a∧b∧c)∨((¬a)∧(¬b))∨((¬b)∧(¬c))