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Lógica matemática/ ¬a&bv(¬b)&c&dv(¬c)&d

Expresión ¬a&bv(¬b)&c&dv(¬c)&d

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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