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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Q: . R is the relation defined on Z as follows: m R n ⇒ 4 | (m² – 1 r (1) Prove that R is an…

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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…

Q: Show that “is unitarily equivalent to” is an equivalence relation on Mn×n(C).

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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: 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: Please help me out

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

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: 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: 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: Show that each of the following relations equivalence classes. on Z is an equivalence relation, and…

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: A relation R on R² is defined by ((x1, y1), (2, 2)) R if Prove that R is an equivalence relation.…

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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…