Sr Examen

Expresión A&¬B&¬Cv(¬AvB)&CvC&¬C

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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