"Let R be the relation defined on Z by aRb if a + b is even. Show that R is an equivalence relation and determine the distinct equivalence classes." I know how to show the equivalence relation, however I have no idea how to approach determining the distinct equivalence classes?

Q: what are the steps you take to find the equivalence classes? I still don't really understand why…

A: To determine the distinct equivalence classes of the relation R defined on Z (the set of integers)…

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A: Given, R is an  equivalence relation onA={a, b, c, d, e, f, g}Such that  aRc, cRd, dRg, bRf

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Q: 3. The DIIOwing relations are not equi properties that are not satisfied. Explain your answer. a. a…

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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…

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Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: 6. Let X = {1,2,3,4, ... ,16}. Define xRy to mean that 5 divides x - y. a) List the elements of R-1.…

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Q: Step 1 of 1 A An equivalence relation R on a set S is one that satisfies these three properties for…

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Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: Give an example of two equivalence relations R and S on

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Q: Multiplication on the number pairs is defined as follows: (a, b) · (c, d) = (ad + bc, ac + bd).& in…

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

Q: And what would be the 15 equivalence relations? And what does "up to isomorphism" mean?

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Q: Let S be the equivalence relation on P({1,2,3,4}) — {0} defined by XSY if and only if max(X) – |X| =…

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Q: Show that the intersection of any collection of equivalence relations over a set A is also an…

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Q: 1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b…

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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…

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Q: 2. Find two verbs or nouns each that are: (a) reflexive (b) transitive (c) symmetric

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Q: roblem 0.2. Which of the following examples are equivalence relations? (1) S is the set of real…

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Q: Show that the following is an equivalence relation: R = {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (3,…

A: Equivalence relations are a fundamental concept in mathematics that allow us to group elements of a…

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

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Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

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: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

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Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

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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: = Give an example of an equivalence relation R on the set A {a, b, c, d, e, f, g, h} such that there…

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Q: What is the significance of the line above the 'a' variable in this context?

A: Given . is nothing but a element of A.And the set is just denoted by, is called the class of . It…

Q: Which of the following statements about equivalence relations and partial ordering is/are ALWAYS…

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Q: Let S be the set of real numbers. If a,be S, define a ~ b if a -b is an integer. Show that is an…

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Q: Please answer the part (B). I have got a solution for the question on this platform but the answer…

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Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Give at least three different examples of equivalence relations.   Note: In every example please…

A: A relation R on a set A is said to be an equivalence relation if and only if the relation R is…

Q: The domain of the following relations is the set of all integers. Determine if the relation R…

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Q: (d) Justifying your answer, find the smallest set of related pairs which must be added to R in order…

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Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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Q: a. Let A = The set of numbers involve in your college ID. And R = {(x, y)1+ 2 divdes (x3 + y} be a…

A: Part (a) Write Cartesian form of set R: A=0,1,3,5,7R=x,y|⇔2 divides…