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Expresión BDv¬(A¬DvA)(Av¬A¬DVBD)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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