1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the relation R in R2² is an equivalence relation or not. If it is not an equivalence relation, justify your answer. If it is an equivalence relation, provide a complete proof.

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: 2. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and suppose R is a relation defined by a is related to b…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

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

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: 4. Let S be a set and RC S × S. Given elements a and b of S we say that a is related to b if (a, b)…

A: Hey, since there are multiple subpart posted, we will answer first 2 questions. If you want any…

Q: 2. For each equivalence relation below, find the requested equivalence class. a. R = { (1,1), (1,…

A: As per our company guidelines we can solve only the first three subparts. Kindly re Post the other…

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: 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: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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Q: Please solve this question. please explain thoroughly. Thanks

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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: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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Q: 3. For universe S = R² define relation ~ as: (a, b) ~ (c,d) ⇒ 2a-b2c - d. Prove that is an…

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Q: 2. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and suppose R is a relation defined by a is related to b…

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Q: Define the relation R on 72 = Z x Z by (a, b) R (c, d) if a + d = b+ c. Prove that R is ar…

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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: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

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: prove why they have or do not have the properties: reflexive, symmetric, antisymmetric, transitive…

A: A=a,b,cR=a,a, b,b, c,c, a,b, a,c, c,b A relation R is reflexive if a,a∈R for every element a. Here…