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Lógica matemática/ ab->c->b!c<->!a

Expresión ab->c->b!c<->!a

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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