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Lógica matemática/ not(not(a)*not(b)*not(c)+not(a)*b*c+a*not(b)*c)

Expresión not(not(a)*not(b)*not(c)+not(a)*b*c+a*not(b)*c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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