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Lógica matemática/ qv(p∧ r)∧¬((pv r)∧ q)

Expresión qv(p∧ r)∧¬((pv r)∧ q)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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