To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence relation.  True or False

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

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Q: 4. Let f : X → Y define a relation on the set X by „Ry if and only if (x) = fy). Is f an equivalence…

A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

Q: Every equivalence relation is reflexive. True False

A: A relation is said to be an equivalence relation if and only if the relation R is reflexive,…

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: PROBLEM1 Instruction: Prove that the relation is  an equivalence relation.  For x, y ∈ R say x is…

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Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

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

A: Let A  = {-1,0,1}×{0,1,2,3}  i.e A=…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

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Q: Let f: X → Y and define x~y if f (x) = f (y). Show that - is an equivalence relation on X.

A: The objective is to show that ~ is an equivalence relation on X.

Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: 4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an…

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Q: B and let R = {(x, y) E A x A | g(x) = g(v)}. Suppose g: A Show that R is an equivalence relation on…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

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Q: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

Q: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

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Q: S is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, rRy if and…

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Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence…

A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Show that the relation R on Z defined by aRb if and only if 5a−3b is even, for a, b ∈ Z, is an…

A: Let R be a relation from a set A to itself. R is said to be an equivalence relation if 1) R is…

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

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Q: Determine whether the following relations are equivalence relations. For those relations that are…

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Q: (a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

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Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

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Q: Let the relation R defined on the set of positive integers as (x, y) ER if 3 divides X - y Determine…

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Q: Let R be a relation defined on Z as follows: (a,b) is an element of R if and only if the square of a…

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Q: For nonempty sets A, B, and C, |A| <= |B| and |B| <= |C|, then |A| <= |C|.

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Q: Determine whether the following relations are equivalence relations. For those relations that are…

A: Consider the given relation is given as:

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 diudes (x −…

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on…

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Q: 2. There is a function f : X →Y . Let's define a relation R in a set X, by a formula: (xRy) → (f(x)…

A: Given f: X → Y and R is the relation in the set X such that x R y ⇔ f(x) = f(y)

Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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Q: A relation R on a set A is backwards transitive if, and only if, for every r, y, z E A, if rRy and…

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Q: Determine, with justification, whether the following relations are equivalence relations. If so,…

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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…

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

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

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Q: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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Q: On P2, define a relation p(x) ~ q(x) if p(0) = q(0). (a) Show that this is an equivalence relation…

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Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the…

A: Let S be a nonempty set. Consider the relation ~ on P(S)  defined by A~B if A∪Bc=S To show: "~" is…

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: equivalence

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Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Q: Prove that the given relation is an equivalence relation, and describe the distinct equivalence…

A: Let A is the set of all students at your college. For every x,y∈A,  xSy⇔x is the same age as y. That…