Determine if the following relations are partial orders, if so, calculate the maximum, minimum, minimum and maximum elements. 1. In Z: a ≤ bif a = 2b. 2. In Z+: a ≤ b if a² = 6². 3. In P(X) (here P(X) denotes the power set of X) A≤ B if ACB. 4. In {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15): ≤y if q EZ exists such that y = qa x

Q: Which of the following relations is a partial order relation defined on A={1,2,3} O a. R =…

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Q: 14. Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A→ B as follows: For all (x, y)…

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Q: 5. For each of the following partial orders, draw a Hasse diagram, find the maximal and minimal…

A: (a) Given, R is a partial order on the set                0, 2, 4, 6, 8, 10 such that (x, y)∈R if…

Q: Let A = follows: For V(a,b), (c,d) € A × A, (a,b)R(c,d) a ≤ c and b <d {0, 1,2} and the partial…

A: Introduction: Relation is the base of studying theory of functions. Every relation can be…

Q: 2. Let x be an element of a convex set S. Assume that x1 = x + €ip E S and x2 = x – €2P E S, where p…

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Q: 5. Let R and S be relations on a set A. Use proof by contradiction to show that if R and S are…

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Q: Let A = follows: For V(a,b), (c,d) = A x A, (a,b)R(c,d) ⇒ a ≤ c and b ≤ d {0,1,2} and the partial…

A: a. The Hasse diagram is shown below.

Q: Find, for each part of the question, an example of a set S and two relations R1 C S x S and R2 C S x…

A: Since the questions contains many subparts. As per the guidelines I am answering the first three…

Q: {2, 4, 6, 8} and define a relation R from A to Bas follows: for all (x,y) E AX B, (x, y) ER T. set…

A: As per our guidelines we are supposed answer only 3 subparts and rest can be reposted Given Data:…

Q: a. xRy x C y

A: Since you have asked multiple question, we can solve first question for you. If you want other…

Q: Dijec not need to prove you function is a bijection): (a) N and Z (b) Rand (1, ∞) (c) (0, 2) and (3,…

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Q: Consider the partial order with domain {3,5,6,7,10,14,20,30,60} and with x ≤ y if x evenly dividesy.…

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Q: Let K = {a, b, c, d, e}. Find, for each part of the question, an example of an object that satisfies…

A: (b) Given vertex set is as follows: K=a, b, c, d, e We are asked to find a 4-colorable graph with…

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: 4. Determine which properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does…

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Q: (4) Let T be the partial order relation on P({1,2,..., 20}) defined by ATB if and only if |A < |B|…

A: Question: Let T be the partial order relation on P1,2,...,20 defined by ATB if and only if A&lt;B or…

Q: (c) 60 70 M 30 14 6 10 | | 3 5 7 2 20 바 30 6 3 60 20 10 | 5 70 14 7

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Q: If X = {a, b, c} , Tx = {0, X, {a},{b, c}}, Y = {x, y, z} and ty = {Ø, Y, {y}} then f = {(a, z), (b,…

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Q: Let A be the set {1,2,3,5,6,8, 10, 12}. Let R be the partial order on A defined so that (a, b) is in…

A: A Hasse diagram is a graphical representation of the relation of elements of a partially ordered set…

Q: 6. (a) Let A, B, be subsets of R. State the conditions which make the pair (A, B) Dedekind cut. (b)…

A: It is given that Let A, B be subsets of R.

Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: 1. Let R be a relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by R = {(a, b) ∈ A × A | 4…

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Q: Which of the following ordered pairs are not in the partial ordering with the accompanying Hasse…

A: Please see the below picture for detailed solution.

Q: Given set A = {1, 2, 3, 4}, mention 5 or more relations (R) defined on A such that R does not…

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Q: Let S = ((a), b, (a, (b)]), c). Which one of the following relations on S is a strict partial order?…

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Q: 1. Give an example of a subset S of the set of all the subsets of 2={a,b,c,d,e}, such that | S=4 and…

A: As you asked more than one question I answered only first one.

Q: Suppose that A and B are sets and f : A –→ B is a function. Fix subsets X,Y C A. Prove that Imf(X) –…

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Q: 5. Let A = {1, 2} and B x+y y) e R such that {3,4}and define a relation from A to B as (x,y) e AxB…

A: We will find out the required values.

Q: 2. Let A, B and C be sets, and let g: A → B and f: B → C be functions. Prove: (i) If f, g are…

A: Answer given below.

Q: Consider relation R={(x,y)|x divides y,xEA,y€A} on the set A={2,3,4,5,10,12,25,30}. (a) Check…

A: We are given a relation : R={(x,y)|x divides y,x∈A,y∈A}  on a set A={2,3,4,5,10,12,25,30}

Q: Let A = {2, 3, 6, 9, 10, 12, 14, 18, 20} and let R be the partial order relation defined on A where…

A: (a) complete the Hasse diagram:

Q: tA {1,2,3,4,5}. Then define the relationR = {(1, 1), (2, 2), (3, 3), (4, = {(x,y) ERXR | |x|+ [y] =…

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Q: Let A = {armadillo, bear, crocodile, dolphin, eagle, fox}. Construct a par- tial ordering < on A…

A: Given the set A=armadillo, bear, crocodile, dolphin, eagle, fox. We need to construct a partial…

Q: Let A = {1,2,3,4}, B = {2,3,4,5}, and C = {2,4,6,8,10}. Suppose R is a 3-ary relation that is…

A: To determine the triples in the array.

Q: 7) Which of the following total orders are compat- ible with the partial order? Choose all which ap-…

A: Note: We are using the convention that the implicit arrows point up. We will verify the total order…

Q: 6.3. Let (A, <A) and (B,<B) be two partially ordered sets. One can define on the cartesian product A…

A: Given: A, ⩽A and B, ⩽B are partially ordered sets.  A Cartesian product A x B is defined with…