Sr Examen

Expresión AvA&(CvB)&(AvB)vB&C

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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