Thread: 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.

Here are the steps. You give the reasons.

Originally Posted by Plato

Here are the steps. You give the reasons.

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

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

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

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

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