Sr Examen

Expresión (¬aavb)&(avc)&(bvc)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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