Sr Examen

Expresión ¬C&(¬AvB)vA&B&C

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    Solución

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