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Lógica matemática/ (a*(c⊕a⊕(a*b)))⊕(b*(c⊕b⊕!(a+b)))

Expresión (a*(c⊕a⊕(a*b)))⊕(b*(c⊕b⊕!(a+b)))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (a∧(a⊕c⊕(a∧b)))⊕(b∧(b⊕c⊕(¬(a∨b))))
    (a∧(a⊕c⊕(a∧b)))⊕(b∧(b⊕c⊕¬(a∨b)))\left(a \wedge \left(a ⊕ c ⊕ \left(a \wedge b\right)\right)\right) ⊕ \left(b \wedge \left(b ⊕ c ⊕ \neg \left(a \vee b\right)\right)\right)
    Solución detallada
    a⊕c⊕(a∧b)=(b∧c)∨(c∧¬a)∨(a∧¬b∧¬c)a ⊕ c ⊕ \left(a \wedge b\right) = \left(b \wedge c\right) \vee \left(c \wedge \neg a\right) \vee \left(a \wedge \neg b \wedge \neg c\right)
    a∧(a⊕c⊕(a∧b))=a∧(b∨¬c)∧(c∨¬b)a \wedge \left(a ⊕ c ⊕ \left(a \wedge b\right)\right) = a \wedge \left(b \vee \neg c\right) \wedge \left(c \vee \neg b\right)
    ¬(a∨b)=¬a∧¬b\neg \left(a \vee b\right) = \neg a \wedge \neg b
    b⊕c⊕¬(a∨b)=(b∧¬c)∨(¬a∧¬c)∨(a∧c∧¬b)b ⊕ c ⊕ \neg \left(a \vee b\right) = \left(b \wedge \neg c\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg b\right)
    b∧(b⊕c⊕¬(a∨b))=b∧¬cb \wedge \left(b ⊕ c ⊕ \neg \left(a \vee b\right)\right) = b \wedge \neg c
    (a∧(a⊕c⊕(a∧b)))⊕(b∧(b⊕c⊕¬(a∨b)))=(a∧b)∨(a∧¬c)∨(b∧¬c)\left(a \wedge \left(a ⊕ c ⊕ \left(a \wedge b\right)\right)\right) ⊕ \left(b \wedge \left(b ⊕ c ⊕ \neg \left(a \vee b\right)\right)\right) = \left(a \wedge b\right) \vee \left(a \wedge \neg c\right) \vee \left(b \wedge \neg c\right)
    Simplificación [src]
    (a∧b)∨(a∧¬c)∨(b∧¬c)\left(a \wedge b\right) \vee \left(a \wedge \neg c\right) \vee \left(b \wedge \neg c\right) 
    (a∧b)∨(a∧(¬c))∨(b∧(¬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 | 0      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FND [src]
    Ya está reducido a FND
    (a∧b)∨(a∧¬c)∨(b∧¬c)\left(a \wedge b\right) \vee \left(a \wedge \neg c\right) \vee \left(b \wedge \neg c\right) 
    (a∧b)∨(a∧(¬c))∨(b∧(¬c))
    FNC [src]
    (a∨b)∧(a∨¬c)∧(b∨¬c)∧(a∨b∨¬c)\left(a \vee b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg c\right) \wedge \left(a \vee b \vee \neg c\right) 
    (a∨b)∧(a∨(¬c))∧(b∨(¬c))∧(a∨b∨(¬c))
    FNCD [src]
    (a∨b)∧(a∨¬c)∧(b∨¬c)\left(a \vee b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg c\right) 
    (a∨b)∧(a∨(¬c))∧(b∨(¬c))
    FNDP [src]
    (a∧b)∨(a∧¬c)∨(b∧¬c)\left(a \wedge b\right) \vee \left(a \wedge \neg c\right) \vee \left(b \wedge \neg c\right) 
    (a∧b)∨(a∧(¬c))∨(b∧(¬c))
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