Give an example of two equivalence relations R and S on

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: S=0,1,2,3×0,1,2=0,0;0,1;0,21.0;1,1;1,22.0;2,1;2,23.0;3,1;3,2

Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

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: Assume that you know that ~ is an equivalence relation on R\ {0} defined as follows: xy > 0. Find…

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Q: Prove that the relation of congruence is an equivalence relation.

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

Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: Let R1 = {(1,1), (2,2)} and R2 = {(1,1), (1, 2)} be relations on A = {1,2}. Then R1 UR

A: In this question given that two sets R1 and R2 and we find the unions  of these sets and relation of…

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: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

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

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…

A: Consider the given information.

Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

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Q: Assume (r1, y1) ~ (x2, Y2) → f(x1,Y1) = f(x2, Y2). Prove that ~ an equivalence relation.

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Q: Prove that "is similar to" is an equivalence relation on Mnxn(F ).

A: We have to prove that “is similar to” is an equivalence relation on Mnxn(F ) i) Every matrix A is…

Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

A: The relation is reflexive, since a,a∈R, where a∈A Also, since a=b where (a,b)∈R therefore, the…

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: True or False? Let R be an equivalence relation on A = {w, x, y, z}. If wRx, yRz, and wRz, then…

A:

Q: Let H be the set of all human beings. Consider the relation R defined on H by xRy if and only if x…

A: R defined on H by xRy if and only if x and y have the same biological mother. reflexivity : x &…

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…

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Q: (a) Show that R is an equivalence relation. (b) List three members of each of the equivalence…

A: Equivalence relation: A relation R is called an equivalence relation in a set A, if it follows the…

Q: Suppose A = {-4,-3,–2,–1,0,1,2,3,4} and R is defined on A by aRb a² - b² is divisible by 4. Prove…

A: A relation R on a set A is said to be an equivalence relation, if it satisfies the following three…

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

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

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Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…

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Q: Let S be a set of distinct symbols. Show that the relation defined onW(S) in this chapter is an…

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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 R be an equivalence relation and let [x] be the equivalence class of x, prove x belong to [x]

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Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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

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

A: Introduction :

Q: Which of these relations on {0, 1, 2, 3} are equivalence ?relations

A: Equivalence relations are the relations which are reflexive (xRx), symmetric (xRy implies yRx),…

Q: The relation defined as x ~ yx ≡ y (mod7) for x, y ∈ Z in Z Write the equivalence classes by writing…

A: Relation R is defined in Z as x≡y(mod 7)  (difference of x and y is multiple of 7) Reflexivity : For…

Q: Define: what is an equivalence relation?

A:

Q: Let R = {(f, g) | f(1) = g(1)} be a relation defined on the set of func- tions from Z to Z. Is R an…

A: Let R be a relation on a set A. Then R is said to be an equivalence relation if it is reflexive,…

Q: 4|(x+3y)

A:

Q: 5. Let a and b be real numbers, not both zero. For (x1, Y1) and (x2, 42) in R², (x1, yı) ~ (x2, y2)…

A: Given that,  a and b are real numbers, not both zero. For By using the definition of equivalence…

Q: Give examples of relations R and S on Z such that  Both R and S are not equivalence relations but R…

A: We need to find two set which are on equivalence on Z but their sum do.  LEet, R= a<b S=a>b…

Q: Let A = {1,2,3,4} and let R = equivalence relation. Determine the equivalence classes.…

A: Given A=1,2,3,4 and R be the relation defined by R=1,1,1,2,2,1,2,2,3,4,4,3,3,3,4,4. We have to show…

Q: Find all equivalence relations on {1,2, 3}.

A: A relation R on a set A is said to be an equivalence relation if it is reflexive symmetric and…

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: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…

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Q: Give examples of relations R and S on Z such that (a) Both R and S are not equivalence relations but…

A: (a) Let R and S be two relations on ℤ such that both R and S are not equivalence relations. Let…