Consistency-related proof in predicate logic

[Mr.Cauliflower]

Could someone please help me with the proof of the following statement?

Let L be language with n different constants and at least one predicate symbol. Prove that there exist 2 different maximal consistent sets formed of closed formulas of the language L.

 

[AKG]

Do you know that if S is a consistent set of sentences (closed formulas), then there exists a maximal consistent extention S' of S (S' is an extention of S in the sense that S' \subseteq S)? To prove that there exist two different maximal consistent sets, find two consistent sets S and T such that any extention S' of S must be different from any extention T' of T.

 

[Mr.Cauliflower]

Do you know that if S is a consistent set of sentences (closed formulas), then there exists a maximal consistent extention S' of S (S' is an extention of S in the sense that S' \subseteq S)?

You're right, I think I found it as Lindenbaum's lemma. Anyway, I don't know how to do this:

find two consistent sets S and T such that any extention S' of S must be different from any extention T' of T.

 

[AKG]

What have you tried? As a hint, it's very very easy. S and T need not be complicated at all.