1. ## logic

My teacher gave me a home work but I couldn't do it.Pls help me

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.

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

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

I'm sorry but I couldn't understand that Could you explain how can you find, pls?For instance where is t?

4. Using 3 & 2, with modus tollens gives not r.

5. 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

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

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.

Here is another proof using contradiction:

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

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

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

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