Sr Examen
Lógica matemática/ avb&a↓b&c&d

Expresión avb&a↓b&c&d

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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