Sr Examen

Expresión (a->b)->((b->c)->(avb->c))

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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