Exercise 7.21

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

  1. Prove using resolution that the above sentence entails $G$.

  2. 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?

  3. 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.

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

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