# Proof of p^(qvr) <=> (p^q)v(p^r)

1. Sep 18, 2008

### evagelos

How do we prove in propositional calculus :

......p^(qvr) <===> (p^q)v(p^r) semantically and syntactically

2. Sep 19, 2008

### CompuChip

Well, what have you already come up with?

3. Sep 19, 2008

### HallsofIvy

Staff Emeritus
Comparing truth tables will do it quickly and neatly. Are you not allowed to use that method?

4. Sep 19, 2008

### CompuChip

I had to Google as well, as far as I can see, using truth tables would be the semantic proof.

5. Sep 19, 2008

### evagelos

Semantical proof without using true tables ,i have one in mind but i am not very positive about it.Then syntactically how about a contradiction you think it could work ,although it looks a bit messy

6. Sep 20, 2008

### CompuChip

It is not quite clear to me what you mean by a semantical proof, and a syntactical one.
Also, if you would post your idea we can have a look at it. Maybe you are on the right track but just need a last push, or maybe you even got it right but lack the confidence