# Natural Deduction in propositional logic

• Aug 6th 2012, 01:15 PM
gomdohri
Natural Deduction in propositional logic
I am trying to solve this but I am not too sure whether I am doing this right

p V ( q ʌ r)
----------
p V q

and I know this can be proved using V-E rule.

But I just don't know the step maybe because i am new to this thing. Please help me..
• Aug 6th 2012, 02:18 PM
emakarov
Re: Natural Deduction in propositional logic
There are several flavors of natural deduction: Fitch style, tree style with formulas as nodes and tree style with sequents as nodes. The following is a derivation in tree style with formulas (the picture is clickable).

Attachment 24444

Fee free to ask further questions if this format is not clear.
• Aug 6th 2012, 10:12 PM
gomdohri
Re: Natural Deduction in propositional logic
if you don't mind could you please represent this in Fitch style so that I can check whether I 've got this right? thank you very much Mr. emakarov!
• Aug 7th 2012, 02:26 AM
emakarov
Re: Natural Deduction in propositional logic
Fitch style is something like this.

Code:

```1. p \/ (q /\ r)        Assumption 2.  p                        Assumption 3.  p \/ q                2, \/I 4.  q /\ r                Assumption 5.  q                        4, /\E 6.  p \/ q                5, \/I 7. p \/ q                1,2-3,4-6, \/E```
• Aug 7th 2012, 07:05 AM
gomdohri
Re: Natural Deduction in propositional logic