Definitions:-
Suppose set is P.
Minimal element:- An element a P is minimal if there is no x P such that a<x. In short these are elements that have no tails in hasse diagram.
Maximal element:- An element a P is maximal if there is no x P such that x < a. In short,these are elements that have no horns in hasse diagram.
Maximum element:- An element a P is greatest or maximum if x <= a for all x P.(note <= is relation).In short if maximal set has only one element then that element becomes maximum else not .also maximum is always unique.
Minimum element :- An element a P is least or minimal if a <= x for all x P. in short,if minimal set list has only one element then that element becomes minimum element.
3. (a Draw a diagram to represent the | (divides) partial order on the set {1,...
please help with this math problem i am very lost on it. thanks! 4. Consider the divisibility partial order on the set 12, 4, 5,6,9, 10, 15, 27,30, 36, 48, 50, 60) Draw the Hasse diagram. Find any greatest elements, least elements, maximal ele- ments, minimal elements. 4. Consider the divisibility partial order on the set 12, 4, 5,6,9, 10, 15, 27,30, 36, 48, 50, 60) Draw the Hasse diagram. Find any greatest elements, least elements, maximal ele- ments, minimal...
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...
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...
Show your work, please 4. Partial Orders Let P be the collection of all subsets of X = {a,b,c,d} that have at least two elements. (So {a,c} € P, but {b} P.) Consider the subset relation C as a partial order on P. For example, {a,b} = {a,b,c}. Draw the Hasse diagram, and find any maximum/minimum elements, and maximal/minimal elements.
9. The "divides" relation defines a partial ordering on the set {1,2,3,6,8,10). Draw the Hasse diagram for this poset. [8 points)
Problem 6. Consider the partial order on a, b, c, d, e, f,g, h\ determined by the fol- lowing Hasse diagram, XI a. and answer the following about (a) Is it true that d g? (b) Find all minimal and maximal elements. c) Are there any maximum elements? d) Find all common upper bounds of e and f (that is, find every q such that eq and f q). e) Find the least upper bound of c and e
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...
7. Sort the following list into lexicographic order using a three-pass bucket sort: 521, 432, 743, 422, 752, 750, 430, 541, 544, 400, 751, 525 8. Let S be the set containing the first ten multiples of three, so S 3,6,9,12, 15, 18, 21, 24,27,30]. Order S with the divides relation. What is the covering relation? Draw the Hasse diagram. List the minimal and maximal elements. Specify a chain of longest length 7. Sort the following list into lexicographic order...
7. 12 M:1.5 M Each Answer these questions for the partial order of Hasse diagram. [CLO # 31 0 0 0 a) Find the maximal elements. b) Find the minimal elements c) Is there a greatest element? d) Is there a least element? e) Find all upper bounds of (A, B, C). f) Find the least upper bound of {A, B, C), if it exists. g) Find all lower bounds of {F, G, H). h) Find the greatest lower bound...
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...