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Lógica matemática/ P→Q→R

Expresión P→Q→R

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    Solución

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