# logic

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• October 23rd 2008, 08:49 AM
scofield
logic
My teacher gave me a home work but I couldn't do it.Pls help me (Doh) (Worried)

Question is here:

1)(¬pvq¬)→r/\s (premise)

2)r→t (premise)

3)¬t (premise)
_________________
.'. p (conclusion)

How can we get the conclusion from using the premises (1,2 and 3)?Show that with using rules of inferences.(Speechless)
• October 23rd 2008, 09:22 AM
Plato
Here are the steps. You give the reasons.
$\begin{gathered}
\neg r \hfill \\
\neg r \vee \neg s \hfill \\
\neg \left( {r \wedge s} \right) \hfill \\
\neg \left( {\neg p \vee \neg s} \right) \hfill \\
p \wedge q \hfill \\
\therefore p \hfill \\
\end{gathered}$
• October 23rd 2008, 09:31 AM
scofield
Quote:

Originally Posted by Plato
Here are the steps. You give the reasons.
$\begin{gathered}
\neg r \hfill \\
\neg r \vee \neg s \hfill \\
\neg \left( {r \wedge s} \right) \hfill \\
\neg \left( {\neg p \vee \neg s} \right) \hfill \\
p \wedge q \hfill \\
\therefore p \hfill \\
\end{gathered}$

I'm sorry but I couldn't understand that (Worried) Could you explain how can you find, pls?For instance where is t?
• October 23rd 2008, 10:04 AM
Plato
Using 3 & 2, with modus tollens gives not r.
• October 23rd 2008, 10:34 AM
scofield
Quote:

Originally Posted by Plato
Using 3 & 2, with modus tollens gives not r.

Ok.Then what about the others?There is :

(¬pV¬q)→r/\s

¬r

I'm so sory but I couldn't understand those steps too (Worried)
• October 23rd 2008, 10:48 AM
poutsos.B
Quote:

Originally Posted by scofield
My teacher gave me a home work but I couldn't do it.Pls help me (Doh) (Worried)

Question is here:

1)(¬pvq¬)→r/\s (premise)

2)r→t (premise)

3)¬t (premise)
_________________
.'. p (conclusion)

How can we get the conclusion from using the premises (1,2 and 3)?Show that with using rules of inferences.(Speechless)

Here is another proof using contradiction:

1) (~pv~q)------> r^s assumption

2) r---->t.....................assumption

3) ~t...........................assumption

4) ~p..........................assumption for contradiction

5) ~pv~q....................from (4) by using Co...........

6) r^s.........................from (1) and (5) by using M..........

7) r..............................from (6) by using A...........

8) t.............................from (2) and (7) by using M............

9) t ^ ~t from (3) and (8) by using Ad................

But t ^ ~t contradiction hence p