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Lógica matemática/ (P→Q)∧R

Expresión (P→Q)∧R

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    Solución

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