Sr Examen

Expresión {¬qv[pv¬(q^p)]}^¬[¬(qvr)v(¬pvq)]

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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