Sr Examen

Expresión (¬P∧Q)→((R∧¬R)∧¬Q)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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