A propositional 2-CNF expression is a conjunction of clauses, each containing exactly 2 literals, e.g.,

(A ∨ B) ∧ (¬ A ∨ C) ∧ (¬ B ∨ D) ∧ (¬ C ∨ G) ∧ (¬ D ∨ G).

a. Prove using resolution that the above sentence entails G.

b. Two clauses are semantically distinct if they are not logically equivalent. How many semantically distinct 2-CNF clauses can be constructed from n proposition symbols?

c. Using your answer to (b), prove that propositional resolution always terminates in time polynomial in n given a 2-CNF sentence containing no more than n distinct symbols.

d. Explain why your argument in (c) does not apply to 3-CNF.