Sr Examen

Expresión е&b&(b&cvc)va&c(a&b)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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