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Lógica matemática/ a(c-b)-b(c-a)+c(b-a)

Expresión a(c-b)-b(c-a)+c(b-a)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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