8. We know that P₁ = P2 on B if P₁ = P₂ on C, provided that C generates B and is a 7-system. Show this last property cannot be omitted. For example, consider 2 = (a, b, c, d) with 1 P₁((a)) = P₁({d})= P2({b)) = P2({c)) = = and
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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2Prove that the digraph obtained from Cay({(1, 0), (0, 1)}:Z4 ⊕ Z7)by deleting the vertex (0, 0) has a Hamiltonian circuit.Consider two points (x0, y0) and (x1, y1). Prove that the first order Langrange polynonial is equivalent to linear interpolation.
- Prove that the Cayley digraph given in Example 6 does not have aHamiltonian circuit. Does it have a Hamiltonian path?Find a Hamiltonian circuit inCay({(a, 0), (b, 0), (e, 1)}:Q4 ⨁ Z3).Suppose that a Hamiltonian circuit exists for Cay({(1, 0), (0, 1)}:Zm ⊕Zn) and that this circuit exits from vertex (a, b) vertically.Show that the circuit exits from every member of the coset(a, b) + <(1, -1)> vertically.
- Suppose that a Hamiltonian circuit exists for Cay({(1, 0), (0, 1)}:Zm ⨁ Zn) and that this circuit exits from vertex (a, b) vertically.Show that the circuit exits from every member of the coset(a, b) + <(1, -1)> verticallyLet D4 = <r, f | r 4 = e = f 2, rf = fr-1>. Verify that6 * [3 * (r, 0), ( f, 0), 3 * (r, 0), (e, 1)]is a Hamiltonian circuit inCay({(r, 0), (f, 0), (e, 1)}:D4 ⨁ Z6).Assuming Get Food Now achieved 12,000 interactions, how many of these would have resulted in customer being less than satisfied with their first interaction?
- 9, 10, 19, 20 using Gauss-Jordan ElimiThe dependencies between the 10 activities listed in the table above are as follows:• The project starts with two activities—A, and B—which can be done concurrently.• When activity A is finished, activity C can start• When activity B is finished, activities D and E can start• When both activities C and D are finished, activity F can start• When activity E is finished, activity G can start• When activity F is finished, activity H can start• When both activities G and H are finished, activity I can start• When activity G is finished, activity J can start• The project is complete when activities I and J are finished Questions1. Organize the information above in an activity precedence table showing the activity, precedent and duration (calculated using the PERT weighted average formula and round to the nearest integer).2. Draw an AON network diagram and calculate its early start, early finish, late start and late finish times, floats (Free and total) for each activity. Make sure you…I need help with all parts of this quesiton 8