How Can Boolean Polynomials Determine Consistency in Propositional Formulas?

[zzmanzz]

My professor wants to convert propositional statements such as X ^ Y into polynomeals such as

P[(X^Y)] = xy

Now, we may have multiple propositional formulas and wish to determine if they are consistent or inconsistent using Boolean polynomials.

I'm having a tough time finding material on this subject online or on you tube. Could someone please give me links to texts or videos where logical propositions are converted to Boolean polynomials and how they are used in proving consistency and inconsistency in a set of propositional formulas.

Also, I have some trouble converting statements such as

[ (p->q) -> (q->r) ] -> (p->r)

into Boolean polynomials.

Again, I'm looking for material covering the above scenarios. It would be much appreciated.

 

[Erland]

Look up Disjunctive normal form.