Sr Examen
Expresión (P→Q)∧((Q→P)→(P→Q))
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Solución
Ha introducido
[src]
(p⇒q)∧((q⇒p)⇒(p⇒q))
$$\left(p \Rightarrow q\right) \wedge \left(\left(q \Rightarrow p\right) \Rightarrow \left(p \Rightarrow q\right)\right)$$
Solución detallada
$$p \Rightarrow q = q \vee \neg p$$
$$q \Rightarrow p = p \vee \neg q$$
$$\left(q \Rightarrow p\right) \Rightarrow \left(p \Rightarrow q\right) = q \vee \neg p$$
$$\left(p \Rightarrow q\right) \wedge \left(\left(q \Rightarrow p\right) \Rightarrow \left(p \Rightarrow q\right)\right) = q \vee \neg p$$
$$q \Rightarrow p = p \vee \neg q$$
$$\left(q \Rightarrow p\right) \Rightarrow \left(p \Rightarrow q\right) = q \vee \neg p$$
$$\left(p \Rightarrow q\right) \wedge \left(\left(q \Rightarrow p\right) \Rightarrow \left(p \Rightarrow q\right)\right) = q \vee \neg p$$
Tabla de verdad
+---+---+--------+ | p | q | result | +===+===+========+ | 0 | 0 | 1 | +---+---+--------+ | 0 | 1 | 1 | +---+---+--------+ | 1 | 0 | 0 | +---+---+--------+ | 1 | 1 | 1 | +---+---+--------+