Sr Examen
Lógica matemática/ Bx(A\C)=(BxA)A(Bx(ANC))

Expresión Bx(A\C)=(BxA)A(Bx(ANC))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (b∧x∧(a|c))⇔(a∧b∧c∧n∧x)
    $$\left(b \wedge x \wedge \left(a | c\right)\right) ⇔ \left(a \wedge b \wedge c \wedge n \wedge x\right)$$

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