Sr Examen

Expresión !(a&b)&cva&b&!cva&cv!avb

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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