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Lógica matemática/ bc¬d+a¬b¬c

Expresión bc¬d+a¬b¬c

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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