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Lógica matemática/ ¬P∨(¬Q∨R)∧(Q∨¬R)

Expresión ¬P∨(¬Q∨R)∧(Q∨¬R)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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