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Lógica matemática/ (d∧(¬(a∨b∨c)))∨(a∧d)∨b

Expresión (d∧(¬(a∨b∨c)))∨(a∧d)∨b

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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