Sr Examen

Expresión (avb∧¬c)∧¬(a∧c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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