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Lógica matemática/ notbnotdornotaandnotbcornotabnotc

Expresión notbnotdornotaandnotbcornotabnotc

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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