Mathematical Logic question

Question

Which among them are valid?

How to approach such questions ?

Comments

All 3 are valid...

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You can apply resolution principle for this kind of questions,you can find it in rosen. Its easy by solving that method instead of remembering a bunch of rules. If you can remember and apply them,its fine .Else read that and try applying.

Answer 1

 

To approach these questions , please study rules of inference

 

Comments

Yes :)  but i also want to know where i went wrong when i tried with  the rules...so want a help with that

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2nd is one of the inference rule known as destructive dilemma.

(r --> s) = (~r v s)

(~q v ~s)

As both s and ~s can't be true simultaneously. This infer that either  ~q or ~r is true.

Now,

(~q v ~r)

(p --> q) = (~p v q)

As again both q and ~q can't be true simultaneously. Any one of them ~p or ~r has to be true.

As from the premises we can reach to the conclusion it is valid.

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got it :)