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Lógica matemática/ CA+¬B↔BC→¬A¬BA→C

Expresión CA+¬B↔BC→¬A¬BA→C

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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