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