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