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