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Lógica matemática/ ab¬cv¬b¬c¬d

Expresión ab¬cv¬b¬c¬d

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    Solución

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