Sr Examen
Expresión ∼((R⇒P)∧(R⇒∼Q))∧∼((∼Q⇒R)∧(P⇒R))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬((p⇒r)∧(¬(q⇒r))))∧(¬((r⇒p)∧(r⇒(¬q))))
$$\neg \left(\left(p \Rightarrow r\right) \wedge q \not\Rightarrow r\right) \wedge \neg \left(\left(r \Rightarrow p\right) \wedge \left(r \Rightarrow \neg q\right)\right)$$
Solución detallada
$$p \Rightarrow r = r \vee \neg p$$
$$q \Rightarrow r = r \vee \neg q$$
$$q \not\Rightarrow r = q \wedge \neg r$$
$$\left(p \Rightarrow r\right) \wedge q \not\Rightarrow r = q \wedge \neg p \wedge \neg r$$
$$\neg \left(\left(p \Rightarrow r\right) \wedge q \not\Rightarrow r\right) = p \vee r \vee \neg q$$
$$r \Rightarrow p = p \vee \neg r$$
$$r \Rightarrow \neg q = \neg q \vee \neg r$$
$$\left(r \Rightarrow p\right) \wedge \left(r \Rightarrow \neg q\right) = \left(p \wedge \neg q\right) \vee \neg r$$
$$\neg \left(\left(r \Rightarrow p\right) \wedge \left(r \Rightarrow \neg q\right)\right) = r \wedge \left(q \vee \neg p\right)$$
$$\neg \left(\left(p \Rightarrow r\right) \wedge q \not\Rightarrow r\right) \wedge \neg \left(\left(r \Rightarrow p\right) \wedge \left(r \Rightarrow \neg q\right)\right) = r \wedge \left(q \vee \neg p\right)$$
$$q \Rightarrow r = r \vee \neg q$$
$$q \not\Rightarrow r = q \wedge \neg r$$
$$\left(p \Rightarrow r\right) \wedge q \not\Rightarrow r = q \wedge \neg p \wedge \neg r$$
$$\neg \left(\left(p \Rightarrow r\right) \wedge q \not\Rightarrow r\right) = p \vee r \vee \neg q$$
$$r \Rightarrow p = p \vee \neg r$$
$$r \Rightarrow \neg q = \neg q \vee \neg r$$
$$\left(r \Rightarrow p\right) \wedge \left(r \Rightarrow \neg q\right) = \left(p \wedge \neg q\right) \vee \neg r$$
$$\neg \left(\left(r \Rightarrow p\right) \wedge \left(r \Rightarrow \neg q\right)\right) = r \wedge \left(q \vee \neg p\right)$$
$$\neg \left(\left(p \Rightarrow r\right) \wedge q \not\Rightarrow r\right) \wedge \neg \left(\left(r \Rightarrow p\right) \wedge \left(r \Rightarrow \neg q\right)\right) = r \wedge \left(q \vee \neg p\right)$$
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 | +---+---+---+--------+