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