Show that there is no formal proof of p → qFp.
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- Give a constructive proof to show that a DFA Mk = (Qk, Σk, δk, q0, Fk) exists that recognizes each Lk = {w: w ends in k 1’s} (for all k > 0) over Σ = {0, 1.Let R=ABCDEGHK and F= {ABK→C, A→DG, B→K, K→ADH, H→GE} . Is it in BCNF? Prove your answer.Prove that (p →(q →r)) → ((p →q) →(p →r)) ≡ T for all propositions p, q, r.
- Let L = { <M> | M is a TM that accepts sR whenever it accepts s } . Show that L is undecidable.Prove that if X is an answer set of a traditional program P so that for some rule A0 ← A1,...,Am, not Am+1,...,not An in P, it holds that {A1,...,Am} is in X and the intersection of {Am+1,..., An} and X is empty, then A0 is in X.For f (a, b) = (a | b) | b(a) Simplify f (a, b).(b) Find DNF for f (a, b).(c) Is f (a, b) satisfiable?
- Show that ∼ p ∧ (p ∧ q) is a contradiction.Match the following sentence to the best suitable answer: - A. B. C. D. for the linear congruence ax=1(mod m), x is the inverse of a, if__________ - A. B. C. D. What is -4 mod 9 ? - A. B. C. D. The solution exists for a congruence ax=b(mod m) such that GCD(a,m)=1 and - A. B. C. D. (107+22)mod 10 is equivalent to :_________ A. 5 B. c divides b C. GCD(a,m)=1 D. 9 mod 10Show that P is closed under union