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Lógica matemática/ (¬S∨P)∧(¬S∨¬Q)∧(P∨Q∨¬R)

Expresión (¬S∨P)∧(¬S∨¬Q)∧(P∨Q∨¬R)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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