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Lógica matemática/ ¬(¬(bvc)v(¬(avc))va*b)

Expresión ¬(¬(bvc)v(¬(avc))va*b)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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