9. The "divides" relation defines a partial ordering on the set {1,2,3,6,8,10). Draw the Hasse diagram...
Given a partial - ordered relation {(a, b) a bisects b} on the set {2, 4, 6, 8, 10, 60, 120, 240). a. Draw a Hasse diagram of poset b. Look for the maximum element. c. Look for the minimal elements. d. If so, look for the greatest element - in the poset? e. If so, look for the smallest element in the poset? f. Find UB from (30, 60) g. Find the LB of (30, 60) h. Find LUB...
The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, H, I, J} D G H E Figure 3: A Hasse diagram shows 10 vertices and 8 edges. The vertices, rep- resented by dots, are as follows: vertex J; vertices H and I are aligned vertically to the right of vertex J; vertices A, B, C, D, and E forms a closed loop, which is to the right of...
Discrete Mathemathics answer #2 1. Let B {a, b} and U P(B). Draw a Hasse diagram for C on U. a. 1, 2, 3, 6}. Show that divides, | b. Let A is a partial ordering on A. Draw a Hasse diagram for divides on A. C. Compare the graphs of parts a and c. d. Answer 2. Repeat Exercise 1 with B {a, b, c} and {1,2, 3,5, 6, 10, 15, 30}. Hint Here is a Hasse diagram for...
10. Verify that the relations given below are quasiorders. List the elements of each equivalence class of the induced equivalence relation, and draw the Hasse (a) On the set (1,2,..., 303, define mn if and only if the sum of the digits (b) On the set (1.2,3,4,11, 12, 13,14,21,22,23,24), define mn if and only diagram for the induced partial order on the equivalence classes of m is less than or equal to the sum of the digits of n. if...
1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the set S defined as follows: Va,bE S, arb if and only if every prime number that divides a is a factor of b and a S b. The relation T is a partial order relation (you do not need to prove this). Draw the Hasse diagram for T 1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the...
3. (a Draw a diagram to represent the | (divides) partial order on the set {1, 2, 3, 4, 5, 6 7,8,9, 10, (b) Identify all minimal, minimum, maximal, and maximum elements in the diagram
Q-4. [8+3+3+3+3 marks] Let be the partial order relation defined on , where means. a) Draw the Hasse diagram for . b) Find all maximal and minimal elements. c) Find lub({6,12}). a) Find glb({6,12}). e) What is the least element? The greatest element? Q-4. [8+3+3+3+3 marks] Let R be the partial order relation defined on A = {2,3, 6, 9, 10, 12, 14, 18, 20}, where xRy means x|y. a) Draw the Hasse diagram for R. b) Find all maximal...
2. A binary string is a finite sequence u-діаг . . . an, where each ai is either 0 or 1. In this case n is the length of the string v. The strings ai, aia2,... ,ai... an-1,ai... an are all prefixes of v. On the set X of all binary strings consider the relations Ri and R2 defined as follows: Ri-(w, v) w and v have the same length ) R2 = {(u, v) I w is a prefix...
Consider the greater than or equal to relation on {0, 1,2,3,4,5). (a) Construct the Hasse diagram for this relation. (b) Give any maximal, minimal, maximum, minimum elements of the relation.
2. A binary string is a finite sequence v = a1a2 . . . an, where each ai is either 0 or 1. In this case n is the length of the string v. The strings a1, a1a2, . . . , a1 . . . an−1, a1 . . . an are all prefixes of v. On the set X of all binary strings consider the relations R1 and R2 defined as follows: R1 = {(w, v) | w...