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Lógica matemática/ ((A&(¬B∨(¬C&D)))∨¬A)&D

Expresión ((A&(¬B∨(¬C&D)))∨¬A)&D

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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