Q.1. Consider the set of sentences below. S1: A -> (BVE). S2: E -> D. S3: CAF -> -B. S4: E -> В. S5: B -> F. S6: B a. Convert the set of sentences into CNF.
Added by Katherine G.
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(a) Prove using resolution that the following sentence entails G: (A ∨ B) ∧ (¬ A ∨ C) ∧ (¬ B ∨ D) ∧ (¬ C ∨ G) ∧ (¬ D ∨ 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.
Akash M.
1. s → (r ∨ q) 2. (r ∨ s) ↔ q 3. (z ∧ s) → p 4. z → (~r → q) 5. (p → r) → ~s
Adi S.
Using natural deduction, show the following: (Please ensure that you make use of only the core inference rules. Do not use sequence introduction rules). a. ~A, A ↔ B ⊢ ~B b. A → (B v C), B → ~D, C → ~D ⊢ A → ~D c. ~A → (B → ~C), ~D → (~C → A), D v ~A, ~D ⊢ ~B d. ~A → (A v (B → A)), (B v C) → ~A, B v C ⊢ C
Sri K.
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