Let X be the set {1, 2, 3, 4, 5} and Rthe "less than" relation on X, that is x Ryif and only if x

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: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

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Q: Let A = {2,3,4,...,17,18). Let R be the equivalence relation on AxA, defined by (a,b)R(c,d) if and…

A: Let A = {2,3,4,.......... 17,18].Let R be the equivalence relation on AXA, defined by (a,b)R(c,d) if…

Q: The relation R on the set of all integer numbers is defined by R = {(x, y) = Z × Z: x - y ≤ 2} is an…

A: Given a relation R on the set of all integer numbers defined by R={(x, y)∈Z×Z:x-y≤2}.  We have to…

Q: a)Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z × Z,…

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Q: uts) Do the following for the set X = {1,2,3,4,5). 7. (a) Give an example of a relation on X that is…

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: The given relation R is as follows. R=x,y∈Z×Z:x is a multiple of y If x,y∈R, we denote x related to…

Q: 4. Let R be a relation on the set of all integers. xRy iff x - y = 3m for some integer m. Show that…

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Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

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Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…

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Q: Let I be the set of all straight lines in the plane. Define and equivalence relation R by x R y iff…

A: Let, R be a relation on L(set of all straight lines in the plane) defined as, xRy iff x and y are…

Q: Given the relation R = {(1,2),(2,3)} on the set A = {1,2,3} . What is the minimum  number of ordered…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: 2. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

A: Let A be a non-empty set. A relation R on A is said to be equivalence relation if it is reflexive…

Q: 1, Let R be the relation defined on the set A = {1, 2, 3, 4, 5, 6,} Such that aRb means a+2 <= b.…

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Q: In each of the following cases of a set X and relation determine whether ~ is reflexive, symmetric,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: In the following questions, determine whether the binary relation is: (1) reflexive, (2) symmetric,…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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Q: Give an example of relation on {1,2,3,4} that is reflexive, not symmetric, and not transitive

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Q: Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3,…

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Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.

Q: 3. Let X be a set and S and R equivalence relations on X. Prove or give a concrete counter example…

A: Since you have asked multiple questions, we will solve the first and second question for you. If you…

Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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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: b) Let A = {1, 2, 3, 4, 5, 6}=B and R be a relation from A to B such that a R b if and only if a is…

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Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…

A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…