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.
Let S = {a, b, c} and consider the poset (P(S), ⊆) where P(S) is the...
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
Question 2 (10%) (a) Draw a poset diagram for the poset P = { φ , { a } , { b } , { c } , { a, b } , { a, c } , { b, c } , { a, b, c }} , with the subset relation. (b) Describe the glb and lub of pairs of elements in terms of set operations. That is, given two elements S and T in the above poset,...
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of these 7 points. We define the following partial order on S: We have (r, y)(', y) iff x< x and y < / Draw the Hasse diagram of S S 6. We consider the same partial order as in Problem 5, but it is now defined on R2....
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,
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.
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...
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.
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...
Let S be the universal set, where: S = {1, 2, 3, ..., 18, 19, 20} Let sets A and B be subsets of S, where: Set A = {2,5, 6, 7, 8, 14, 18} Set B = {1, 2, 3, 4, 7, 9, 10, 11, 12, 14, 18, 19, 20} Find the following: The cardinality of the set (A U B): n(AUB) = The cardinality of the set (A n B): n(An B) is You may want to draw...
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...