How to convert to conjunctive normal form?
If i have a formula:
$(\neg Q\land P) \lor (\neg Q\land R) \lor (Q \land \neg P \land \neg R) \lor (\neg P \land \neg R)$
The formula is in disjunctive normal form. I don't know which rule to use.
I tried to use distribution rule as stated here but i would end up at 24 members which i don't think is the correct way to do this.
Best Answer
Well, you can do what you sad: just 'multiply' them all out; it'll give you 24 terms, but many can be removed through various simplification principles.
In fact, one of those simplification principles is:
Absorption
$P \land (P \lor Q) \Leftrightarrow P$
$P \lor (P \land Q) \Leftrightarrow P$
You can apply this to your original expression, since $\neg P \land \neg R$ will 'absorb' $Q \land \neg P \land \neg R$, and therefore your original expression can immediately be simplified to just:
$(\neg Q\land P) \lor (\neg Q\land R) \lor (\neg P \land \neg R)$
OK, and now applying Distribution will 'only' give you $8$ terms ... that's not so bad, is it?