Sr Examen

Expresión (b+c+d+e+g)*(f+g)*d*(a+e+f)*(a+b+c)*(b+c+d)*(a+b+e)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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