Show your work, please 4. Partial Orders Let P be the collection of all subsets of...
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...
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...
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.
Consider the poset S = ({P{1,2,3} - {0}), S) (a) List any minimal elements (b) If it exists give the minimum element (c) List any maximal elements (d) If it exists give the maximum element (e) Give the Hasse diagram for S
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
Discrete Mathematics. Let A = {2,3,4,6,8,9,12,18}, and define a relation R on A as ∀x,y ∈ A,xRy ↔ x|y. (a) Is R antisymmetric? Prove, or give a counterexample. (b) Draw the Hasse diagram for R. (c) Find the greatest, least, maximal, and minimal elements of R (if they exist). (d) Find a topological sorting for R that is different from the ≤ relation.
. Let C be a collection of open subsets of R. Thus, C is a set whose elements are open subsets of R. Note that C need not be finite, or even countable. (a) Prove that the union U S is also an open subset of R. SEC (b) Assuming C is finite, prove that the intersection n S is an open subset of R. SEC (c) Give an example where C is infinite and n S is not open....
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
Let S = {a, b, c} and consider the poset (P(S), ⊆) where P(S) is the power set of S (set of all subsets of S). 1) Draw the Hasse Diagram of (P(S), ⊆) and draw the Hasse Diagram of a Topological Sorting of (P(S), ⊆). Thank you.
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...