Sr Examen

Expresión !a*b+a*!b*!c*!d*b+!a*!b*!c+!a*!c+(!b+!a*!b*!c+!b)*(b*c*d+b*!c+b*c*!d)+!a*c*!d+!a*!b*c+!a*c*d+!a*b+!a*!b*!c

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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