1. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence re- lation that the others lack. a) {(0, 0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)} c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3,3)}

Q: R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3),(2,4),(3,1)}; S =…

A:

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

A:

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: 3. Which of the following is an equivalence relation? Explain. (a) lives in the same city as (b) is…

A: Due to Bartleby answering guidelines I have solved only question no 3. Because you didn't mention…

Q: NXN set on " (a,b)~ (c,d) -) a+d -b+c %3D define d as, equiualence relation? Shaw Is reation ""

A:

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

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

A:

Q: Let a relation ∼ on R2 = {(a, b): a, b ∈ R} be defined as: (a, b) ∼ (c, d) if and only if | a | + |…

A:

Q: Please help me out

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

Q: 2 Relations For the following relation R over the integers, prove whether R is or is not: 1.…

A:

Q: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: Prove relation B is an equivalence relation

A:

Q: 1) Let S be the equivalence relation on R defined by xSy iff x-y Q. Then a) [√3]-(-√3+r,req) b)…

A:

Q: 3) a) Suppose A = {0,1,2,3,4} and R = {(0,0). (0,4).(1.1), (1,3).(2,2).(3,1).(3,3),(4,0).(4,4)} is…

A:

Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

A:

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: Let A = {p , q, r, s, t, u, v}, and let R be the following equivalence relation on A: R = { (p, p)…

A:

Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

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: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: (3) Let S be the equivalence relation on {0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A:

Q: Let be the equivalence relation on Z defined by z~ y if and only if z-y is divisible by 15. Give…

A: Equivalence relation

Q: 2. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

A: Let A be a non-empty set. A relation R on A is said to be equivalence relation if it is reflexive…

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

A: Given that A= { 1 , 2 , 3 , 4 , 5 , 6} And the equivalence relation on A R = { (1,1) ,(2,2) ,(3,3)…

Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

A:

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…

A:

Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

A:

Q: There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (1) {(0,…

A:

Q: A// Which of these relations on {0, 1 , 2, 3 } are equivalence relations, why? a) R1= {(0, 0). (1 ,…

A: According to our guidelines we can answer only first question and rest can be reposted.

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

A:

Q: 1) Let R be the relation on Z+ such that (p, q) R(r, s) if and only if p- s = q ·r. That is, the…

A:

Q: Equivalence relation of

A: Let A = {0,1,2,3...} and define  relation  R = {(m, n); m^3 ≡ n^3 mod 3} we need to show that R…

Q: d) ((f g)| for some CEZ, for all xE Z, f(x) – g(x) = C} e) {f, 8) | f(0) = g(1) and f(1) = g(0)}

A: Part (d) From the given information: The relation is . Here, C is constant.

Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.

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

A: The relations on 0, 1, 2, 3 are given as: (a) 0, 0, 0, 2, 2, 0, 2, 2, 2, 3, 3, 2, 3, 3 (b) 0, 0, 0,…

Q: 4- The orthogonal relation is A: symmetric and reflective relation B: symmetric and not reflective…

A: