Sr Examen
Lógica matemática/ ¬a*¬b*¬c*d+¬a*¬b*c*d+¬a*b*¬c*¬d+¬a*b*c*¬d+a*¬b*¬c*d+a*¬b*c*d+a*b*¬c*¬d+a*b*c*¬d

Expresión ¬a*¬b*¬c*d+¬a*¬b*c*d+¬a*b*¬c*¬d+¬a*b*c*¬d+a*¬b*¬c*d+a*¬b*c*d+a*b*¬c*¬d+a*b*c*¬d

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (a∧b∧c∧(¬d))∨(a∧c∧d∧(¬b))∨(a∧b∧(¬c)∧(¬d))∨(a∧d∧(¬b)∧(¬c))∨(b∧c∧(¬a)∧(¬d))∨(c∧d∧(¬a)∧(¬b))∨(b∧(¬a)∧(¬c)∧(¬d))∨(d∧(¬a)∧(¬b)∧(¬c))
    $$\left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(a \wedge d \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg a \wedge \neg d\right) \vee \left(b \wedge \neg a \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right)$$
    Solución detallada
    $$\left(a \wedge b \wedge c \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(a \wedge d \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg a \wedge \neg d\right) \vee \left(b \wedge \neg a \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right) = \left(b \wedge \neg d\right) \vee \left(d \wedge \neg b\right)$$
    Simplificación [src]
    $$\left(b \wedge \neg d\right) \vee \left(d \wedge \neg b\right)$$ 
    (b∧(¬d))∨(d∧(¬b))
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
    FNDP [src]
    $$\left(b \wedge \neg d\right) \vee \left(d \wedge \neg b\right)$$ 
    (b∧(¬d))∨(d∧(¬b))
    FND [src]
    Ya está reducido a FND
    $$\left(b \wedge \neg d\right) \vee \left(d \wedge \neg b\right)$$ 
    (b∧(¬d))∨(d∧(¬b))
    FNCD [src]
    $$\left(b \vee d\right) \wedge \left(\neg b \vee \neg d\right)$$ 
    (b∨d)∧((¬b)∨(¬d))
    FNC [src]
    $$\left(b \vee d\right) \wedge \left(b \vee \neg b\right) \wedge \left(d \vee \neg d\right) \wedge \left(\neg b \vee \neg d\right)$$ 
    (b∨d)∧(b∨(¬b))∧(d∨(¬d))∧((¬b)∨(¬d))
    © Sr Examen