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Lógica matemática/ Pv(~P->(Qv(~Q->R)))

Expresión Pv(~P->(Qv(~Q->R)))

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    Solución

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