Sr Examen

Expresión x⇒(y⇒z)⇒(x*y⇒z)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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