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Expresión abc+abd+abe+acd+ace+¬(a+d+e)+(¬b¬cd)+(¬b¬ce)+(¬b¬d¬e)+(¬b¬d¬e)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

    Ha introducido [src]
    (a∧b∧c)∨(a∧b∧d)∨(a∧b∧e)∨(a∧c∧d)∨(a∧c∧e)∨(¬(a∨d∨e))∨(d∧(¬b)∧(¬c))∨(e∧(¬b)∧(¬c))∨((¬b)∧(¬d)∧(¬e))
    (abc)(abd)(abe)(acd)(ace)(d¬b¬c)(e¬b¬c)(¬b¬d¬e)¬(ade)\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge b \wedge e\right) \vee \left(a \wedge c \wedge d\right) \vee \left(a \wedge c \wedge e\right) \vee \left(d \wedge \neg b \wedge \neg c\right) \vee \left(e \wedge \neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d \wedge \neg e\right) \vee \neg \left(a \vee d \vee e\right)
    Solución detallada
    ¬(ade)=¬a¬d¬e\neg \left(a \vee d \vee e\right) = \neg a \wedge \neg d \wedge \neg e
    (abc)(abd)(abe)(acd)(ace)(d¬b¬c)(e¬b¬c)(¬b¬d¬e)¬(ade)=(ac)(ad)(ae)(¬b¬c)(¬a¬d¬e)\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge d\right) \vee \left(a \wedge b \wedge e\right) \vee \left(a \wedge c \wedge d\right) \vee \left(a \wedge c \wedge e\right) \vee \left(d \wedge \neg b \wedge \neg c\right) \vee \left(e \wedge \neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d \wedge \neg e\right) \vee \neg \left(a \vee d \vee e\right) = \left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)
    Simplificación [src]
    (ac)(ad)(ae)(¬b¬c)(¬a¬d¬e)\left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)
    (a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
    Tabla de verdad
    +---+---+---+---+---+--------+
    | a | b | c | d | e | result |
    +===+===+===+===+===+========+
    | 0 | 0 | 0 | 0 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 0 | 0 | 0 | 0 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 0 | 0 | 0 | 1 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 0 | 0 | 0 | 1 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 0 | 0 | 1 | 0 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 0 | 0 | 1 | 0 | 1 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 0 | 1 | 1 | 0 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 0 | 1 | 1 | 1 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 0 | 0 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 0 | 0 | 1 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 0 | 1 | 0 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 0 | 1 | 1 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 1 | 0 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 1 | 0 | 1 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 1 | 1 | 0 | 0      |
    +---+---+---+---+---+--------+
    | 0 | 1 | 1 | 1 | 1 | 0      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 0 | 0 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 0 | 0 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 0 | 1 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 0 | 1 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 1 | 0 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 1 | 0 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 1 | 1 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 0 | 1 | 1 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 0 | 0 | 0 | 0      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 0 | 0 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 0 | 1 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 0 | 1 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 1 | 0 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 1 | 0 | 1 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 1 | 1 | 0 | 1      |
    +---+---+---+---+---+--------+
    | 1 | 1 | 1 | 1 | 1 | 1      |
    +---+---+---+---+---+--------+
    FNCD [src]
    (a¬b¬d)(a¬b¬e)(a¬c¬d)(a¬c¬e)(cde¬a¬b)\left(a \vee \neg b \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg e\right) \wedge \left(a \vee \neg c \vee \neg d\right) \wedge \left(a \vee \neg c \vee \neg e\right) \wedge \left(c \vee d \vee e \vee \neg a \vee \neg b\right)
    (a∨(¬b)∨(¬d))∧(a∨(¬b)∨(¬e))∧(a∨(¬c)∨(¬d))∧(a∨(¬c)∨(¬e))∧(c∨d∨e∨(¬a)∨(¬b))
    FND [src]
    Ya está reducido a FND
    (ac)(ad)(ae)(¬b¬c)(¬a¬d¬e)\left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)
    (a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
    FNDP [src]
    (ac)(ad)(ae)(¬b¬c)(¬a¬d¬e)\left(a \wedge c\right) \vee \left(a \wedge d\right) \vee \left(a \wedge e\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg d \wedge \neg e\right)
    (a∧c)∨(a∧d)∨(a∧e)∨((¬b)∧(¬c))∨((¬a)∧(¬d)∧(¬e))
    FNC [src]
    (a¬a¬b)(a¬a¬c)(a¬b¬d)(a¬b¬e)(a¬c¬d)(a¬c¬e)(ac¬a¬b)(ac¬a¬c)(ac¬b¬d)(ac¬b¬e)(ac¬c¬d)(ac¬c¬e)(ad¬a¬b)(ad¬a¬c)(ad¬b¬d)(ad¬b¬e)(ad¬c¬d)(ad¬c¬e)(ae¬a¬b)(ae¬a¬c)(ae¬b¬d)(ae¬b¬e)(ae¬c¬d)(ae¬c¬e)(acd¬a¬b)(acd¬a¬c)(acd¬b¬d)(acd¬b¬e)(acd¬c¬d)(acd¬c¬e)(ace¬a¬b)(ace¬a¬c)(ace¬b¬d)(ace¬b¬e)(ace¬c¬d)(ace¬c¬e)(ade¬a¬b)(ade¬a¬c)(ade¬b¬d)(ade¬b¬e)(ade¬c¬d)(ade¬c¬e)(cde¬a¬b)(cde¬a¬c)(cde¬b¬d)(cde¬b¬e)(cde¬c¬d)(cde¬c¬e)\left(a \vee \neg a \vee \neg b\right) \wedge \left(a \vee \neg a \vee \neg c\right) \wedge \left(a \vee \neg b \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg e\right) \wedge \left(a \vee \neg c \vee \neg d\right) \wedge \left(a \vee \neg c \vee \neg e\right) \wedge \left(a \vee c \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee \neg b \vee \neg e\right) \wedge \left(a \vee c \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee \neg c \vee \neg e\right) \wedge \left(a \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee d \vee \neg b \vee \neg e\right) \wedge \left(a \vee d \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee \neg c \vee \neg e\right) \wedge \left(a \vee e \vee \neg a \vee \neg b\right) \wedge \left(a \vee e \vee \neg a \vee \neg c\right) \wedge \left(a \vee e \vee \neg b \vee \neg d\right) \wedge \left(a \vee e \vee \neg b \vee \neg e\right) \wedge \left(a \vee e \vee \neg c \vee \neg d\right) \wedge \left(a \vee e \vee \neg c \vee \neg e\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg b \vee \neg e\right) \wedge \left(a \vee c \vee d \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg c \vee \neg e\right) \wedge \left(a \vee c \vee e \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee e \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee e \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee e \vee \neg b \vee \neg e\right) \wedge \left(a \vee c \vee e \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee e \vee \neg c \vee \neg e\right) \wedge \left(a \vee d \vee e \vee \neg a \vee \neg b\right) \wedge \left(a \vee d \vee e \vee \neg a \vee \neg c\right) \wedge \left(a \vee d \vee e \vee \neg b \vee \neg d\right) \wedge \left(a \vee d \vee e \vee \neg b \vee \neg e\right) \wedge \left(a \vee d \vee e \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee e \vee \neg c \vee \neg e\right) \wedge \left(c \vee d \vee e \vee \neg a \vee \neg b\right) \wedge \left(c \vee d \vee e \vee \neg a \vee \neg c\right) \wedge \left(c \vee d \vee e \vee \neg b \vee \neg d\right) \wedge \left(c \vee d \vee e \vee \neg b \vee \neg e\right) \wedge \left(c \vee d \vee e \vee \neg c \vee \neg d\right) \wedge \left(c \vee d \vee e \vee \neg c \vee \neg e\right)
    (a∨(¬a)∨(¬b))∧(a∨(¬a)∨(¬c))∧(a∨(¬b)∨(¬d))∧(a∨(¬b)∨(¬e))∧(a∨(¬c)∨(¬d))∧(a∨(¬c)∨(¬e))∧(a∨c∨(¬a)∨(¬b))∧(a∨c∨(¬a)∨(¬c))∧(a∨c∨(¬b)∨(¬d))∧(a∨c∨(¬b)∨(¬e))∧(a∨c∨(¬c)∨(¬d))∧(a∨c∨(¬c)∨(¬e))∧(a∨d∨(¬a)∨(¬b))∧(a∨d∨(¬a)∨(¬c))∧(a∨d∨(¬b)∨(¬d))∧(a∨d∨(¬b)∨(¬e))∧(a∨d∨(¬c)∨(¬d))∧(a∨d∨(¬c)∨(¬e))∧(a∨e∨(¬a)∨(¬b))∧(a∨e∨(¬a)∨(¬c))∧(a∨e∨(¬b)∨(¬d))∧(a∨e∨(¬b)∨(¬e))∧(a∨e∨(¬c)∨(¬d))∧(a∨e∨(¬c)∨(¬e))∧(a∨c∨d∨(¬a)∨(¬b))∧(a∨c∨d∨(¬a)∨(¬c))∧(a∨c∨d∨(¬b)∨(¬d))∧(a∨c∨d∨(¬b)∨(¬e))∧(a∨c∨d∨(¬c)∨(¬d))∧(a∨c∨d∨(¬c)∨(¬e))∧(a∨c∨e∨(¬a)∨(¬b))∧(a∨c∨e∨(¬a)∨(¬c))∧(a∨c∨e∨(¬b)∨(¬d))∧(a∨c∨e∨(¬b)∨(¬e))∧(a∨c∨e∨(¬c)∨(¬d))∧(a∨c∨e∨(¬c)∨(¬e))∧(a∨d∨e∨(¬a)∨(¬b))∧(a∨d∨e∨(¬a)∨(¬c))∧(a∨d∨e∨(¬b)∨(¬d))∧(a∨d∨e∨(¬b)∨(¬e))∧(a∨d∨e∨(¬c)∨(¬d))∧(a∨d∨e∨(¬c)∨(¬e))∧(c∨d∨e∨(¬a)∨(¬b))∧(c∨d∨e∨(¬a)∨(¬c))∧(c∨d∨e∨(¬b)∨(¬d))∧(c∨d∨e∨(¬b)∨(¬e))∧(c∨d∨e∨(¬c)∨(¬d))∧(c∨d∨e∨(¬c)∨(¬e))