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Lógica matemática/ ¬[(S→¬P)∧¬R]

Expresión ¬[(S→¬P)∧¬R]

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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