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Lógica matemática/ p^~q^rvp^q^rvp^~q^(~rvp)^q^~rv~p^q^~rv~p^q^rvq^~r^(~pvr)vq^r

Expresión p^~q^rvp^q^rvp^~q^(~rvp)^q^~rv~p^q^~rv~p^q^rvq^~r^(~pvr)vq^r

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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