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