Sr Examen

Expresión ab+(c+a)ab+ac

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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