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Lógica matemática/ ¬a⇒((p*q)⇒r)

Expresión ¬a⇒((p*q)⇒r)

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    Solución

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