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Assume you have a CNF with n different propositional symbols distributed into clauses where each clause has precisely two members. (a) How many such two-member

Assume you have a CNF with n different propositional symbols distributed into clauses where each clause has precisely two members.

(a) How many such two-member clauses can be constructed given the restriction that no two clauses can be logically equivalent?

(b) Prove that when given a CNF of this particular form the runtime of propositional resolution algorithm is a polynomial function of n.

(c) Assume that we are now dealing with CNFs where each clause is of size > 2 (all clauses are still logically non-equivalent). Will the runtime of propositional resolution algorithm still be polynomial in n?

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