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Lógica matemática/ AB+D(!A)+(!A)(!C)+(BD)+B(!C)

Expresión AB+D(!A)+(!A)(!C)+(BD)+B(!C)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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