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Lógica matemática/ ¬b∧c⇔¬a∨b⇒a∧¬c(¬A∨b∧¬c)∧¬(c⇒a)

Expresión ¬b∧c⇔¬a∨b⇒a∧¬c(¬A∨b∧¬c)∧¬(c⇒a)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (c∧(¬b))⇔((b∨(¬a))⇒(a∧(¬c)∧(¬(c⇒a))∧((¬a)∨(b∧(¬c)))))
    (c∧¬b)⇔((b∨¬a)⇒(a∧¬c∧c⇏a∧((b∧¬c)∨¬a)))\left(c \wedge \neg b\right) ⇔ \left(\left(b \vee \neg a\right) \Rightarrow \left(a \wedge \neg c \wedge c \not\Rightarrow a \wedge \left(\left(b \wedge \neg c\right) \vee \neg a\right)\right)\right)
    Solución detallada
    c⇒a=a∨¬cc \Rightarrow a = a \vee \neg c
    c⇏a=c∧¬ac \not\Rightarrow a = c \wedge \neg a
    a∧¬c∧c⇏a∧((b∧¬c)∨¬a)=Falsea \wedge \neg c \wedge c \not\Rightarrow a \wedge \left(\left(b \wedge \neg c\right) \vee \neg a\right) = \text{False}
    (b∨¬a)⇒(a∧¬c∧c⇏a∧((b∧¬c)∨¬a))=a∧¬b\left(b \vee \neg a\right) \Rightarrow \left(a \wedge \neg c \wedge c \not\Rightarrow a \wedge \left(\left(b \wedge \neg c\right) \vee \neg a\right)\right) = a \wedge \neg b
    (c∧¬b)⇔((b∨¬a)⇒(a∧¬c∧c⇏a∧((b∧¬c)∨¬a)))=b∨(a∧c)∨(¬a∧¬c)\left(c \wedge \neg b\right) ⇔ \left(\left(b \vee \neg a\right) \Rightarrow \left(a \wedge \neg c \wedge c \not\Rightarrow a \wedge \left(\left(b \wedge \neg c\right) \vee \neg a\right)\right)\right) = b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right)
    Simplificación [src]
    b∨(a∧c)∨(¬a∧¬c)b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) 
    b∨(a∧c)∨((¬a)∧(¬c))
    Tabla de verdad 
    +---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 1      |
+---+---+---+--------+
| 0 | 0 | 1 | 0      |
+---+---+---+--------+
| 0 | 1 | 0 | 1      |
+---+---+---+--------+
| 0 | 1 | 1 | 1      |
+---+---+---+--------+
| 1 | 0 | 0 | 0      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FNC [src]
    (a∨b∨¬a)∧(a∨b∨¬c)∧(b∨c∨¬a)∧(b∨c∨¬c)\left(a \vee b \vee \neg a\right) \wedge \left(a \vee b \vee \neg c\right) \wedge \left(b \vee c \vee \neg a\right) \wedge \left(b \vee c \vee \neg c\right) 
    (a∨b∨(¬a))∧(a∨b∨(¬c))∧(b∨c∨(¬a))∧(b∨c∨(¬c))
    FND [src]
    Ya está reducido a FND
    b∨(a∧c)∨(¬a∧¬c)b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) 
    b∨(a∧c)∨((¬a)∧(¬c))
    FNCD [src]
    (a∨b∨¬c)∧(b∨c∨¬a)\left(a \vee b \vee \neg c\right) \wedge \left(b \vee c \vee \neg a\right) 
    (a∨b∨(¬c))∧(b∨c∨(¬a))
    FNDP [src]
    b∨(a∧c)∨(¬a∧¬c)b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right) 
    b∨(a∧c)∨((¬a)∧(¬c))
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