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Expresión (abc)∨(a¬bc)∨(¬abc)∨(¬a¬bc)∨(¬a¬b¬c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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