Sr Examen
Lógica matemática/ ab!c!d+!a!b!c!d+abcd+a!bc!d+!abc!d

Expresión ab!c!d+!a!b!c!d+abcd+a!bc!d+!abc!d

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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