Show that the following compound propositions are logically equivalent without the use of truth tables. (ii) (tvs) v (~t^ s) and t (i) pq and (pvq) v (p ^ q) (iii) p^(ps) ^ (s→t) and p^s^t
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- Answer the given question with a proper explanation and step-by-step solution. Which color scheme would be the best to use to show the total population by state, showing states with the fewest number of people to the most, low to high on a choropleth (i.e. shaded or “filled”) map? 1.Diverging 2.Categorical 3.Sequential 4.Sequential-CategoricalConsider the following knowledge base in first order logic: p(X) ← q(X) ∧ r(X, Y ) q(X) ← s(X) ∧ r(Y, Y ) s(a) r(a, a) What is the result of the query p(a) using a backward chaining inference algorithm? Show the intermediary queries.Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root α = 2. Show that 2 is a primitive root of 11. If user A has public key YA = 9, what is A’s private key XA? If user B has public key YB = 3, what is the secret key K shared with A?
- ¬P ∧¬Q≡¬(P ∨Q) Prove the following equivalency relation (Proof, Justification/explanation):Using Armstrong's axioms plus union and decomposition, prove the following: Given attribute sets A, B, C, and D, if A→D and C→B, B→A and D→C then B,D→A,C.Compare and contrast NP and P, and use real-world examples to highlight their differences.
- The set of letters S consists of 30 As, 6 Bs, 24 Cs, 15 Ds, and 15 Es. The set of letters T consists of 25 As, 20 Bs, 15 Cs, 5 Ds and 35 Es. What is the mutual index of coincidence between sets S and T? Leave your answer as a fraction in lowest termsPlease answer this question and plz don't reject it under complex questionConsider the following knowledge base Prove that Q is true with: 1. P → Q 2. L ∧ M → P 3. B ∧ L → M 4. A ∧ P → L 5. A ∧ B → L 6. A 7. B Forward-Chaining Backward-Chaining Resolution Prove t → s: 1. p → q 2. [q ∧ r] → s 3. [t ∧ u] → r 4. u → w 5. t → y 6. y → u 7. r → p 8. p → m i. Express in clause form ii. Forward-Chaining iii. Backward-Chaining iv. Resolution
- Let c1, c2, and c3 be the confidence values of the rules {p}->{q}, {p}->{q, r}, and {p, r}->{q}, respectively. If we assume that c1, c2, and c3 have different values, what are the possible relationships that may exist among c1, c2, and c3? Which rule has the lowest confidence?prove the equivalence of the schemata:~(~(p • ~ q ) • ~ ( ~ p• q)) equal to ~(p • q) • ~(~p • ~q)May I see the 5 samples from the Bayesian network and then using these 5 samples to answer the following query: P(S = s1|L = l1) =?