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Expresión ¬(¬(AB)C∨¬(A∨¬B)¬C)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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