# Propositional Logic | Rewrite Rules | Formula to DNF

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## 33 Replies - 4347 Views - Last Post: 12 July 2012 - 11:06 AM

### #31 TechSyndrome

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## Re: Propositional Logic | Rewrite Rules | Formula to DNF

Posted 12 July 2012 - 10:45 AM

TechSyndrome, on 12 July 2012 - 10:37 AM, said:

sepp2k, on 12 July 2012 - 10:15 AM, said:

Here the negation wasn't part of the pattern that was being replaced. The rule said "replace F->G" with "not F or G". So the solution replaced "S -> R" with "not S or R". The not in front of the parentheses remained unaffected.

If the rule had said "replace not(F -> G) with not F or G" instead, the not would have been removed.

If I understood correctly, the parentheses make quite a difference?

Quote

If the rule had said "replace ¬ (F -> G) with ¬ F or G" instead, the not would have been removed.

The ¬ ("not") would have been removed outside the parentheses, but, a ¬ ("not") would have been added to the "s" inside the parentheses.

So, ¬(S -> R) becomes (¬S -> R) with the above rule ^?

This post has been edited by TechSyndrome: 12 July 2012 - 10:46 AM

### #32 sepp2k

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## Re: Propositional Logic | Rewrite Rules | Formula to DNF

Posted 12 July 2012 - 10:54 AM

No, in the second case the not would have been removed because it was part of the pattern not because of the parentheses. The first pattern didn't contain a not anywhere - the second did. That's why the not disappears in the second case - not because of the parentheses.

### #33 TechSyndrome

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## Re: Propositional Logic | Rewrite Rules | Formula to DNF

Posted 12 July 2012 - 10:59 AM

sepp2k, on 12 July 2012 - 10:54 AM, said:

No, in the second case the not would have been removed because it was part of the pattern not because of the parentheses. The first pattern didn't contain a not anywhere - the second did. That's why the not disappears in the second case - not because of the parentheses.

Ok, do you get the sense that I'm lacking basic knowledge in this, and if so, do you have a reference (YouTube link etc), where I can see where this is all going wrong. Out of everything I've done in Propositional Logic so far, it has been very easy, but something seems to have gone wrong here. I think theres some fundamental topic I've missed out?

### #34 sepp2k

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## Re: Propositional Logic | Rewrite Rules | Formula to DNF

Posted 12 July 2012 - 11:06 AM

I don't know. I don't think there's something specific you're missing (or if you do, I don't know what it is) - just maybe a general familiarity with abstract thinking. But that kind of thing is trained - not learned.