6. Consider the relation R on Z defined by xRy iff x – y= 4n for some n Ɛ Z. (a) Show that R is an equivalence relation? (b) How many equivalent classes are there?

Q: (b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive?…

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A: This is a problem of relation.

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A: A relation R is said to be antisymmetric if (a,b)∈R and (b,a)∈R implies a=b

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Q: Define a relation on R by a ~ b iff aª – b² = bª – a². (a) Show that ~ is an equivalence relation.…

A: (a). To show that the given relation is an equivalence relation, we need to show that it is…

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Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (x, y)R(z, w)…

A: We will find out the required values.

Q: 4. (a) Let R be the set of all real numbers. Consider a relation S on R, i.e. SCRX R. which is…

A: Thank you

Q: 2. Determine the equation of the following function. State your answer as a piecewise function. y 10…

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Q: Consider the relation being described by the following arrow diagram. Which of the these statements…

A: (i) It is given that ;      S = {6, 7, 8}  and  T = {2, 4, 6} And the relation between S and T is :…

Q: 4. Show that the relation defined on Z as follows are equivalence relation (a) For all, n € Z, m R n…

A: Note that : Since you have posted  multiple questions, we will provide the solution only to the…

Q: Define a relation on Z as follows: For m, n € Z, m~n ⇒ 5|(m - n). (5.1) Prove that is an equivalence…

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Q: Please help me out

A: Equivalence Classes: The set S is divided into equivalence classes by ~, which is an equivalence…

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Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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Q: Let R be the relation on the all integers given by xRy iff x- y 2k for some integer k. (1) Prove…

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Q: (29) Let~ be the relation on R given by y Prove that is an equivalence relation on R. Find [].…

A: A relation ~ on the set of real numbers R is defined as x~y if and only if x-y∈Z. Our aim is to show…

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: consider the relation R on R, where R = {(a, b) | a ≤ b+1}. (a) Is the relation R reflexive,…

A: i.Let  then So the relation  holds for all .So  is reflexive.ii.Since the relation is reflexive so…

Q: Prove relation B is an equivalence relation

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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: Define a relation on Q by a b if a-b= for some k, n € Z and n > 0. (i). Prove that it is an…

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Q: 4. Describe all Consider the relation R on R x R defined by (x1, y1) R(x2, y2) iff x₁ - 2y2 = x₂ -…

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Q: ) Let A = {1,2,3, 4} × {1,2, 3, 4}, and define a relation R on A by (1, Yı)R(x2, Y2) if r1 + y1 = x2…

A: Equivalence relation means it should satisfy reflexive, symmetric, Transitive conditions.…

Q: (a) Show that R is an equivalence relation. (b) List three members of each of the equivalence…

A: Equivalence relation: A relation R is called an equivalence relation in a set A, if it follows the…

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A: In the given question we have to find the equivalence classes.

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: Please show the following question in detail: " Let S be a nonempty subset of Z and let R be a…

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Q: (1) Show v is an equivalence relation on S. (2) Describe the equivalence classes of . (3) Describe…

A: Given: Define ~ on S=a, b: a, b∈ℤ, b≠0 by a, b~c, d if and only if ad-bc=0. To show: 1) ~ is an…

Q: 1. X = {1, 2, 3, 4, 5} and Y = {3, 4}. Let's define a relation R in a set P(X), by a formula: (ARB)…

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Q: Suppose that we are interested to count the number of integers not divisible by 7, 8, 9 between 1 to…

A: To find the integers between 1 to 10000 that are not divisible by 7,8 and 9. Firstly, find the L.C.M…

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Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

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Q: (Relations) Consider the set A = {1,2, 3, 4, 5}, and a relation R defined by x Ry + x² – y is an…

A: Since you have posted a multipart question and we can answer three subparts. So, answered the first…

Q: 1. For the set of all integer numbers Z one defines a relation R on Z as R = {(a, b)|a - b- 2 is…

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