Sr Examen
Expresión ((~P∨Q)∧(Q→P))→(~P→~Q)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
((q⇒p)∧(q∨(¬p)))⇒((¬p)⇒(¬q))
$$\left(\left(q \Rightarrow p\right) \wedge \left(q \vee \neg p\right)\right) \Rightarrow \left(\neg p \Rightarrow \neg q\right)$$
Solución detallada
$$q \Rightarrow p = p \vee \neg q$$
$$\left(q \Rightarrow p\right) \wedge \left(q \vee \neg p\right) = \left(p \wedge q\right) \vee \left(\neg p \wedge \neg q\right)$$
$$\neg p \Rightarrow \neg q = p \vee \neg q$$
$$\left(\left(q \Rightarrow p\right) \wedge \left(q \vee \neg p\right)\right) \Rightarrow \left(\neg p \Rightarrow \neg q\right) = 1$$
$$\left(q \Rightarrow p\right) \wedge \left(q \vee \neg p\right) = \left(p \wedge q\right) \vee \left(\neg p \wedge \neg q\right)$$
$$\neg p \Rightarrow \neg q = p \vee \neg q$$
$$\left(\left(q \Rightarrow p\right) \wedge \left(q \vee \neg p\right)\right) \Rightarrow \left(\neg p \Rightarrow \neg q\right) = 1$$
Tabla de verdad
+---+---+--------+ | p | q | result | +===+===+========+ | 0 | 0 | 1 | +---+---+--------+ | 0 | 1 | 1 | +---+---+--------+ | 1 | 0 | 1 | +---+---+--------+ | 1 | 1 | 1 | +---+---+--------+