Sr Examen

Expresión ¬(P∨¬(Q∧R))∨(¬(P∨Q)∧R)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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