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Lógica matemática/ BA∨CAB∨¬(¬(A→BC)≡(AB∨C)→CB)

Expresión BA∨CAB∨¬(¬(A→BC)≡(AB∨C)→CB)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (a∧b)∨(a∧b∧c)∨(¬((¬(a⇒(b∧c)))⇔((c∨(a∧b))⇒(b∧c))))
    $$\left(a \wedge b\right) \vee \left(a \wedge b \wedge c\right) \vee \left(\left(c \vee \left(a \wedge b\right)\right) \Rightarrow \left(b \wedge c\right)\right) \not\equiv a \not\Rightarrow \left(b \wedge c\right)$$
    Solución detallada
    $$a \Rightarrow \left(b \wedge c\right) = \left(b \wedge c\right) \vee \neg a$$
    $$a \not\Rightarrow \left(b \wedge c\right) = a \wedge \left(\neg b \vee \neg c\right)$$
    $$\left(c \vee \left(a \wedge b\right)\right) \Rightarrow \left(b \wedge c\right) = \left(b \wedge c\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(\neg b \wedge \neg c\right)$$
    $$\left(\left(c \vee \left(a \wedge b\right)\right) \Rightarrow \left(b \wedge c\right)\right) ⇔ a \not\Rightarrow \left(b \wedge c\right) = \neg b \wedge \left(a \vee c\right) \wedge \left(\neg a \vee \neg c\right)$$
    $$\left(\left(c \vee \left(a \wedge b\right)\right) \Rightarrow \left(b \wedge c\right)\right) \not\equiv a \not\Rightarrow \left(b \wedge c\right) = b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right)$$
    $$\left(a \wedge b\right) \vee \left(a \wedge b \wedge c\right) \vee \left(\left(c \vee \left(a \wedge b\right)\right) \Rightarrow \left(b \wedge c\right)\right) \not\equiv a \not\Rightarrow \left(b \wedge c\right) = b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right)$$
    Simplificación [src]
    $$b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right)$$ 
    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      |
+---+---+---+--------+
    FNCD [src]
    $$\left(a \vee b \vee \neg c\right) \wedge \left(b \vee c \vee \neg a\right)$$ 
    (a∨b∨(¬c))∧(b∨c∨(¬a))
    FNDP [src]
    $$b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right)$$ 
    b∨(a∧c)∨((¬a)∧(¬c))
    FNC [src]
    $$\left(a \vee b \vee \neg a\right) \wedge \left(a \vee b \vee \neg c\right) \wedge \left(b \vee c \vee \neg a\right) \wedge \left(b \vee c \vee \neg c\right)$$ 
    (a∨b∨(¬a))∧(a∨b∨(¬c))∧(b∨c∨(¬a))∧(b∨c∨(¬c))
    FND [src]
    Ya está reducido a FND
    $$b \vee \left(a \wedge c\right) \vee \left(\neg a \wedge \neg c\right)$$ 
    b∨(a∧c)∨((¬a)∧(¬c))
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