Sr Examen
Lógica matemática/ (¬(¬A*¬B*¬C+¬A*B*C))*(¬(A*B*¬C))+(¬(¬B+¬(¬(A*C)+A*C+A*¬B)))

Expresión (¬(¬A*¬B*¬C+¬A*B*C))*(¬(A*B*¬C))+(¬(¬B+¬(¬(A*C)+A*C+A*¬B)))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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