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Lógica matemática/ ¬c&¬dv¬a&b&¬cvav¬a&b&¬d

Expresión ¬c&¬dv¬a&b&¬cvav¬a&b&¬d

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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