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Lógica matemática/ q->!p*q->a

Expresión q->!p*q->a

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    Solución

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