Q-4. [8+3+3+3+3 marks] Let be the partial order relation defined on , where means. a) Draw...
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.
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...
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...
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.
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...
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...
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
8. Let S = {1, 2, 3, 4). With respect to the lexicographic order based on the usual less than relation, (a) find all pairs in S x S less than (2,3) (b) find all pairs in Sx S greater than (3, 1) (c) draw the Hasse diagram of the poset (SxS,
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
4. Let 3 be the relation on Z2 defined by (a,b) 3 (c,d) if and only if a Sc and b < d. (a) Prove that is a partial order. (b) Find the greatest lower bound of {(1,5), (3,3)}. (c) Is < a total order? Justify your answer.