Which of these relations on {0, 1, 2, 3} are?equivalence relationsa) {(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)}

Answered: Image /qna-images/answer/fbb58ee8-3cba-461e-94c9-0970356807a5.jpg

Which of these relations on {0, 1, 2, 3} are * ?equivalence relations а) ((0, 0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)} с) (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)}

Which of these relations on {0, 1, 2, 3} are * ?equivalence relations а) ((0, 0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)} с) (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)}

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

See similar textbooks

Related questions

Q: Let A = {0,1,2,3} and R be the relation on A given by R =…

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: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: 1. This relation satisfies all the conditions of equivalence relation i.e reflexive, symmetric and…

Q: {0, 1, 2, 3, 4, ...} and define the relation - on A by: x~y if x – y is divisible by 3 Determine…

Q: The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1,…

A: Infinite sets can also be grouped into equivalence classes, such that all the sets in a given…

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

Q: Let A = {1, 2, 3, 4, 6). Let Ri be a relation defined on A. a. Verify reflexive property on the…

Q: Let A = {1, 2, 3, 4}. Let R be the relation on A defined as follows: R = {(1, 1), (1, 2),…

Q: Consider two fuzzy relations [! 0.1 0.3] R=0.8 0.6 0.9 and S=0.2 0.4 0.9 0 03 0.2 0.5 0.7 0,2 0.7…

A: Let R1 and R2 be two fuzzy relations. The max-min composition of R1 and R2 is defined as follows.…

Q: The relation…

A: Given: R is a relation from A to A such that A=1,2,3,4,5 &…

Q: Let R be the relation {(1,2),(1,3),(2,3),(2,4),(3,1)}, and let S be the relation…

Q: The equivalence class of -2 for the relation congruence modulo 5 is о (... -11, -6, —1,4, 9, 14,…

A: Second option is correct.

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: Exercise 5.2.1: Here are two relations: R(A, B): {(0,1), (2,3), (0,1), (2,4), (3,4)} S(B,C): {(0,1),…

A: Given: a. Compute πA+B, A2, B2R A B A+B A2 B2 0 1 1 0 1 2 3 5 4 9 0 1 1 0 1 2 4 6 4 16…

Q: Let A be the set A-(1, 2, 3} The binary relation R={(1,2), (2,1), (1,3), (3,1), (1,1), (3,3) }…

A: Given: A = 1, 2, 3 and R = (1, 2), (2, 1), (1, 3), (3, 1), (1, 1), (3, 3).

Q: Exercise 3.13. Let f: A+B be a one-to-one correspondence. By Exercise 3.12, f-: B A is also a…

Q: Let R1 and R2 be the relations on {1,2,3,4} given by R1 = {(1,1), (1,2), (3,4), (4,2)} R2 =…

Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that - Let A={2,4} and B = {1,3,5}

Q: ii. Determine whether the relation, R = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} is: Yes/No…

Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

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: 7. Compute gfg, the conjugate pair of f by g for f= (2, 3, 5, 4) and g = (1, 3, 2)(4, 5).

Q: The equivalence class of -1 for the relation congruence modulo 5 is O {...,-12, –7, –2, 3,8, 13,…

Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on 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: Let A = {1, 2, 3, 4, 5} and R be the relation defined by R = {(1,1), (2,2), (2,4), (2,5),…

Q: Which of these relations on {O, 1, 2, 3} are ?equivalence relations а) (0, 0), (1, 1), (2, 2), (3,…

Q: Let A={1,2,3,4,5,6} and let R be the equivalence relation on A defined by…

A: Two elements are in same equivalence class if they have an equivalence relation. Given :…

Q: Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows R = {(0, 1), (1,1), (2,…

A: The given sets are -…

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}. How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: Which of these relations on (0, 1, 2, 3} are equivalence relations? o {(0, 0), (0, 1). (0, 2), (1,…

Q: Let S = (0, 1, 2, 3} and the relations A, B, and C on S are as follows: %3D A = {(0, 0), (0, 1), (0,…

Q: 3) Let A = {1, 2, 3, 4, 5, 6, 7, 8}. How many possible symmetric relations over A contain the…

A: Given A=1,2,3,4,5,6,7,8 contains the ordered pair 2,3,3,24,7,5,5 and 8,7 Since, for the diagonal…

Q: let A={0,1,2}. let R = { (0,0),(1,1),(2,2),(0,1),(1,0)}. Is R an equivalnce relation on A?if it is…

A: Given: A=0,1,2 The relation R on set A is defined by R=0,0,1,1,2,2,0,1,1,0 To determine: Whether R…

Q: Which of these relations on {0,1,2,3} are equivalence relations or a partial order? Determine the…

Q: What is the composite

A: Let A,B and C be three sets. Suppose that R is a relation from A to B, and S is a relation from B to…

Q: Let R = {(0,1), (0,2), (1,1), (1,3), (2,2), (3,0)} Find R', the transitive closure of R

Q: The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is: O…

Q: The number of equivalence relations on the set {1, 2, 3, 4} is

A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~ is defined by, "x1,x2~x3,x4 only if…

Q: The relation R on set A = {0, 1, 2, 3, 4, 5} is given by R = {(0, 0), (0, 1), (0, 5)(1,0),(1, 1),…

Q: 1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check…

Q: A = {1,2,3,4,6,8,12} a.) Relation on Z Refleksif Symmetric Transitive

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…

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: Let S = (0, 1, 2, 3} and the relations A, B, and C on S are as follows: A = {(0, 0), (0, 1), (0, 3),…

Q: The binary relation {(1,1), (2,1), (2,2), (2,3), (3,1), (3,2)} on the set {1, 2, 3} is O reflexive,…

A: Relation

Question

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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.
Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .
Prove that the equalities in Exercises hold for all in . Assume only the basic postulates for and those properties proved in this section. Subtraction is defined by .
Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
Which of these relations on {0,1,2,3} are equivalence relations or a partial order? Determine the properties of an equivalence relation or partial order 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)} e. {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,2),(3,3)}
Which of these relations on {0, 1, 2, 3} are equivalence relations? *
True or False? Let R be an equivalence relation on A = {w, x, y, z}. If wRx, yRz, and wRz, then xRy.
Let A = {0,1,2,3} and R a relation over A: R = {(0,0),(0,1),(0,3),(1,1),(1,0),(2,3),(3,3)} Check whether R is an equivalence relation or a partial order. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation or a partial order.
Let A = {0,1,2,3} and R be the relation on A given by R = {(0,0),(0,2),(1,1),(1,2),(2,1),(2,0),(3,1),(2,2),(2,3),(3,2)}. Is R reflexive, symmetric, transitive, antisymmetric?
Let A = {1, 2, 3, 4, 6}. Let Ri be a relation defined on A. a. Verify reflexive property on the relation R1= {(1, 1), (1, 2), (2, 2), (3, 3), (3, 4), (4, 4), (6, 6)}.b. Verify symmetric property on the relation R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 4), (4, 3), (4, 4)}.c. Verify asymmetric property on the relation R3 = {(1, 2), (2, 4), (3, 4), (4, 6), (6, 6)}.d. Verify antisymmetric property on the relation R4 = {(1, 1), (1, 2), (2, 3), (3, 3), (3, 4), (6, 3)}e. Verify transitive property on the relation R5 = {(1, 2), (1, 3), (1, 6), (2, 3), (3, 4), (4, 6), (3, 6)}.
Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive
let A={0,1,2}. let R = { (0,0),(1,1),(2,2),(0,1),(1,0)}. Is R an equivalnce relation on A?if it is what are equivalence classes