Sr Examen
Expresión [(~p→q)∧~(q→p)∨r]→q∧~p
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(r∨(((¬p)⇒q)∧(¬(q⇒p))))⇒(q∧(¬p))
$$\left(r \vee \left(\left(\neg p \Rightarrow q\right) \wedge q \not\Rightarrow p\right)\right) \Rightarrow \left(q \wedge \neg p\right)$$
Solución detallada
$$\neg p \Rightarrow q = p \vee q$$
$$q \Rightarrow p = p \vee \neg q$$
$$q \not\Rightarrow p = q \wedge \neg p$$
$$\left(\neg p \Rightarrow q\right) \wedge q \not\Rightarrow p = q \wedge \neg p$$
$$r \vee \left(\left(\neg p \Rightarrow q\right) \wedge q \not\Rightarrow p\right) = r \vee \left(q \wedge \neg p\right)$$
$$\left(r \vee \left(\left(\neg p \Rightarrow q\right) \wedge q \not\Rightarrow p\right)\right) \Rightarrow \left(q \wedge \neg p\right) = \left(q \wedge \neg p\right) \vee \neg r$$
$$q \Rightarrow p = p \vee \neg q$$
$$q \not\Rightarrow p = q \wedge \neg p$$
$$\left(\neg p \Rightarrow q\right) \wedge q \not\Rightarrow p = q \wedge \neg p$$
$$r \vee \left(\left(\neg p \Rightarrow q\right) \wedge q \not\Rightarrow p\right) = r \vee \left(q \wedge \neg p\right)$$
$$\left(r \vee \left(\left(\neg p \Rightarrow q\right) \wedge q \not\Rightarrow p\right)\right) \Rightarrow \left(q \wedge \neg p\right) = \left(q \wedge \neg p\right) \vee \neg r$$
Tabla de verdad
+---+---+---+--------+ | p | q | r | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+
FNC
[src]
$$\left(q \vee \neg r\right) \wedge \left(\neg p \vee \neg r\right)$$
(q∨(¬r))∧((¬p)∨(¬r))
FNCD
[src]
$$\left(q \vee \neg r\right) \wedge \left(\neg p \vee \neg r\right)$$
(q∨(¬r))∧((¬p)∨(¬r))