5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R= {(a,a), (b,b), (c,c), (d,d)} on S = {a, b, c, d}.

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1, 2} defined by (a, b)S(c, d) if and…

A: S=0,1,2,3×0,1,2=0,0;0,1;0,21.0;1,1;1,22.0;2,1;2,23.0;3,1;3,2

Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: 1. This relation satisfies all the conditions of equivalence relation i.e reflexive, symmetric and…

Q: 8. Draw the directed graph of the binary relation S on B = { a, b, c, d, e} by S = {(a, b),(b,…

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Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

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Q: 4. a) Define the following terms: i) POSETS ii) Equivalence relation

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 9.24. Let R be an equivalence relation on A = {a, b, c, d, e, f,g} such that a Rc, c Rd, d Rg and b…

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Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: Below is the Hasse diagram for a partial order relation R on the set {a, b, c, d, e}. e d be C Are…

A: Introduction: Hasse diagram is very significant in graphing a relation. In this diagram, the…

Q: {(a, b) acb, a and b are finite set of integers}

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Q: 1. Give and example of: (a) a binary relation that is reflexive, transitive, not symmetric and not…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: State whether each of the following statements is true or false. counter example to justify your…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Let

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Q: The universal relation A x A on A is an equivalence relation anti-symmetric a partial ordering…

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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|…

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Q: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

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

A: A partial order relation is total order relation if each of the pair of the elements are comparable.…

Q: Show that the number of equivalence relation in the set {1, 2, 3} containing(1, 2) and (2, 1) is…

A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R?  Note: Select the order that…

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Q: Let A = {1, 2, 3, 4, 5, 6} and R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 3), (3, 2)}.…

A:

Q: 1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by: %3D aRb + a = bc and b= ad,…

A: The given set is A=0,1,2,3,4 and the relation is defined as aRb⇔a=bc and b=ad (a) Check whether R an…

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

A: Here given that the set is A = {a, b, c, d} and the relation on A is given by R = {(a, c), (b, b),…

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: Let RR be a binary relation on A={a,b,c}A={a,b,c} given by…

A: We check relationship is reflexive or not

Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

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Q: For non empty binary relation R={(a, a),(a, b),(b, a),(b, b),(c, c),(c, d),(d, c),(d, d)} on the set…

A: We have to solve given problem:

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

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Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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Q: For every nonempty set A, there exists a relation R which is both an equivalence relation and a…

A: A relation R is said to be equivalence relation if R is Reflexive ,Symmetric and Transitive . R is…

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 diudes (x −…

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Q: d b

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Which of these relations on {0,1,2,3} are equivalence relations or a partial order? Determine the…

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

Q: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

A: Given a relation, aRb⇔ab≤0. To check whether R is an equivalence relation on set ℤ. A relation is an…

Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

A:

Q: 7.3.4 (a) Let - be the relation defined on Z by a~ b + a +b is even. Show that ~ is an equivalence…

A: Since the second question is independent of the first question I am answering the first question…

Q: 13. Let R C R XR with {(x, y)|x2 =, y?}. Characterize R in terms of whether it is reflexive,…

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Q: 1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check…

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Q: 2. Given a relation, R on A = {a, b, c, d} on as follows: %3D R = {(a, a), (a, b), (a, d), (b, b),…

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Q: 5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence…

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Q: Consider the set A={a,b,c,d,e,f}. Define a partial ordering on A by setting x<=y if (x,y) belongs to…

A: Consider the set A={a,b,c,d,e,f}. Define a partial ordering on A by setting x&lt;=y if (x,y) belongs…

Q: Let A = {1,2,3,4} and let R = equivalence relation. Determine the equivalence classes.…

A: Given A=1,2,3,4 and R be the relation defined by R=1,1,1,2,2,1,2,2,3,4,4,3,3,3,4,4. We have to show…

Q: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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Q: Suppose an equivalence relation R has the following equivalence classes that partition the set X.…

A: The ordered pairs in the equivalence relations produced by the given partitions {0, 2}, {1}, {3, 4}.…

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: Consider the set A = {2, 3, 5, 7}. Create a relation R on A that is a partial order with at least…

A: The given set is  A=2,3,5,7 and we have to define a partial order relation R on set A with at least…

Q: 9.16. Let A = {a, b, c, d}. How many relations defined on A are reflexive, symmetric and transitive…

A: given A=a,b,c,d claim- how many realations defined on A are reflexive , symmetric and transitive and…

Q: Let 2 be a non-empty set. (a) Show that the inclusion relation in P (2) is an crder relation…

A: A partial order relation leads to poset which is very interesting.