8) Let A = {2,3,4, 5}, R is defined on A such that (aRB) if and only if (a2 +B+a) is an even number. Prove that R is an equivalence relation on A. NOTE: a = 3

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: Explain why each of the following binary relations on S = {1, 2, 3} is not an equivalence relation…

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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: (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: ~ Define an equivalence relation on Z by a b if a - b is even. Show that . equivalence relation.…

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Q: Given two equivalence relations R and P on A. Prove that (R ∪ P) ^+ is an equivalence relation

A: Given R and P are equivalence relations.Let a∈AAs R and P are reflexive relations, hence (a,a)∈R and…

Q: b) Check whether the relation R on the set S = {1, 2, 3} with the the matrix 1 1 1 0 1 1 1 1 1 is an…

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Q: A relation R is defined on Z by xRy if and only if 8 divides 3x + 5y. Prove that R is an equivalence…

A: This is a question from relation.

Q: Let A = {1, 2, 3, 4, 5, 6}, and consider the following equivalence relation on A: R = {(1, 1),  (2,…

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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 ~ CX *X be an equivalence relation on a set X. For x EX define x := := {x |x E X} is a partition…

A: This is a question from Relation.

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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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: Show that if R and R2 are equivalence relations on A, then R1 n R2 is an equivalence relation on A.

A: Equivalence relation on a set A

Q: 2. Define a relation R on Z as follows: a Rb if and only if 5 | (a²-b²). a) Prove that R is an…

A: A relation R on ℤ is defined by: a R b if and only if 5 | a2-b2 . We have to prove that R is an…

Q: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and…

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: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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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…

A: Given problem is :

Q: 1. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

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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: Let the relation R on the set Z be given by the condition: (x, y) E Rif and only if x4 = y4. Answer…

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Q: Suppose 1 and ₂ are equivalence relations on a set A. Let ~ be defined by the condition that a~ b if…

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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: Let X = {1, 2, 3, 4, 5, 6}. Which of the following could be an equivalence class of an equivalence…

A: Equivalence class on a set

Q: Define a relation R on the set of natural numbers defined by (z, v) E R#z-yis divisible by 3. a)…

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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: Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈…

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Q: A relation R is defined on Z by mRn ⟺ 3m − 7n is even.  a). Prove that R is an equivalence…

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Q: 6. (a, b), C

A: Let R be the relation on the set of ordered pairs of positive integers such that a,b,c,d∈R if and…

Q: a ) Let R be the relation on the set A={1,2,3,4} defined by aRb if and only if 2a>b+1. Find the…

A: let A={1,2,3,4}   aRb iff 2a>b+1   first we will find R…

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…