Expresión (!a*b)+(a*!b*!c*!d*b)+(!a*!b*!c)+(!a*!c)+((!b+!a*!b*!c+!b))*((b*c*d+b*!c+b*c*!d))+(!a*c*!d)+(!a*!b*c)+(!a*c*d)+(!a*b)+(!a*!b*!c)
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$a \wedge b \wedge \neg b \wedge \neg c \wedge \neg d = \text{False}$$
$$b \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \neg b = 1$$
$$\left(b \wedge \neg c\right) \vee \left(b \wedge c \wedge d\right) \vee \left(b \wedge c \wedge \neg d\right) = b$$
$$\left(b \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \neg b\right) \wedge \left(\left(b \wedge \neg c\right) \vee \left(b \wedge c \wedge d\right) \vee \left(b \wedge c \wedge \neg d\right)\right) = b$$
$$\left(b \wedge \neg a\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(\left(b \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \neg b\right) \wedge \left(\left(b \wedge \neg c\right) \vee \left(b \wedge c \wedge d\right) \vee \left(b \wedge c \wedge \neg d\right)\right)\right) \vee \left(c \wedge d \wedge \neg a\right) \vee \left(c \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg d\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge \neg b \wedge \neg c \wedge \neg d\right) = b \vee \neg a$$
Tabla de verdad
+---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1 |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1 |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1 |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1 |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1 |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1 |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1 |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1 |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0 |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0 |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0 |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0 |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1 |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+--------+
Ya está reducido a FND
$$b \vee \neg a$$
Ya está reducido a FNC
$$b \vee \neg a$$