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Lógica matemática/ (P→Q)∧(Q→R)

Expresión (P→Q)∧(Q→R)

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    Solución

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