4. Draw the Hasse Diagram for the following partial orderings. (a) S = {a, b, c} and ρ = {(a, a),(b, b),(c, c),(a, b),(b, c),(a, c)} (b) S = {a, b, c, d} and ρ = {(a, a),(b, b),(c, c),(d, d),(a, b),(a, c)} (c) S = {∅, {a}, {a, b}, {c}, {a, c}, {b}} and AρB ↔ A ⊆ B.

Use the set notation to describe resolution as a refutation system.

In many cases, problem sets that are stated over strictly nominal feature sets do not lend themselves well to classification strategies that are based on vector spaces. Please tell me how much you agree or disagree with this statement. If you were doing ML classification on nominal data, which approach would you employ? Please respond to both of the questions posed above with detailed explanations.

How many states does the composition of (figure 2.) have?

Write the general form of the ARIMA(p, d, q) model. What do the values p, d, and q representin this equation?

For problem sets that are given over purely nominal feature sets, classification methods based on vector spaces are not always the best solution. I'm curious as to how strongly you agree or disagree with this statement. If you were doing ML classification on nominal data, which approach would you use? Provide detailed explanations for your answers to the two questions posed.

5. Let S = {a,b,c,d}, T = {a, c, e, f}, R = {c, f}. Find the following sets.... (a) SUT (b) SnT (c) SU (TNR) (d) T-R (e) Sketch a Venn diagram showing how S, T, and R relate to each other. (f) Let f: R→ R be given by f (x) = 3x - 2. Prove that f (x) is one-to-one and onto.

Let R be an equivalence relation on A = {0,5,7,9} and R = {(0, 9), (0, 5), (7, 7), (9, 5), (5,9), (9, 9), (5, 0), (0, 0), (9, 0), (5,5)}. Answer each of the following questions. (5) = 0 [9] = [0] = [7] =