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Expresión (¬(ab)⇒cd)⇒¬a∨¬(bc)∨¬d

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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