Which ONE of the following represents an equivalence relation on the set of integers? Vx.y€Z, xRy if and only if 2|-y) 2|- 2)

Q: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

Q: 5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}. Define a relation R on S as follows:…

A: Any Relation is said to be equivalent if  it Reflexive , Symmetric and Transitive

Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b): a is a…

A: Given  Set  = set of all natural numbers N Relation = R = { (a,b) : a is multiple of b }   A…

Q: The relation on the set of integers R {(x, y) : 5 divides a- y} is O a. an equivalence relation O b.…

A:

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

A:

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: we have given a set  A = { 1, 2, 3, 4}  and R is a relation on the set A where R is defined as (a,…

Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

A: We have to find the equivalence of the given function and we are also given with the set in which…

Q: Let A = { 2, 3, 4, 6 } and B = { 6, 8, 10 } and define a relation R from A to B as follows: For all…

A: Given that : A = {2, 3, 4,6} and B = {6,8,10} define relation  A*B→R R = {(x ,y): yx is an integer ,…

Q: Let S be the set of real numbers. If a, b e S, define a - b if a – b is an integer. Show that ~ is…

A: Definition of the equivalence relation helps to prove the required. A relation is said to be an…

Q: (a) We have defined the relations =6 and =10 to be certain subsets of Z². Their intersection R=…

A:

Q: 1. Let A = {0,1,2,3,4,5}. Write out the relation R that expresses greater than orequal on A. Then…

A: Handwriting solution

Q: n R m in Z if nm>0

A: 1) reflexive property : for all n in Z - {0}, we have, n R n because, n•n = n² > 0 But, for n = 0…

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: 10) Which of the following statements is false? a) fR is reflexive, then RnRep b) ROR' p R is…

A:

Q: Show which of each of the three properties "reflexive, symmetric, and transitive" apply to each of…

A:

Q: 6f) For the set X = {m,n, p, q,r, s}, let R be a relation on P(X) (the power set of X), given by A R…

A: Yes , this is correct. The set X= {m, n, p, q, r, s} |X|=6 The power set P(X)={ {}, {m}, {n},…

Q: Consider the following relation R on the set Give an example of a pair that is not in R, but in the…

A:

Q: Define a relation R on Z as follows: For all integers m and n, m R n 5| (m² – n²). a. Is 1 R (–9)?…

A:

Q: Let A = { 2, 3, 4} and B = { 6, 8, 10 } and define a relation R from A to B as follows: For all…

A: Using relation property,

Q: Given the following relations on the set {1, 2, 3} and R = {(1, 1), (1, 2), (2, 1), (1,3)}. Which of…

A: Given problem:- Given the following relations on the set {1, 2, 3} and R = {(1, 1), (1, 2), (2, 1),…

Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by a R b if and only if a < b. (a) Compute R²…

A: use the concept of composition          R2=RoR          R3=R2oR

Q: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that  x is congurent to y mod 4.

Q: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b) : |a –…

A: Given: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b)…

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

A:

Q: Let R be the relation, {(a, b) e N x N:a + b is odd}. Give an example that shows that R is not…

A: Given R be the relation, {(a, b) ∈ N x N:a + b is odd}.  We find an example that shows that R is not…

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b}.…

A:

Q: Let R be the relation, {(a, b) e N x N:a + b2 is divisible by 3}. Give an example that shows that R…

A: Symmetric Relation

Q: Characterize the relations in questions 14 and 15 in terms of whether each is reflexive,…

A:

Q: Which of the following relations E are equivalence relations on the set of integers Z? a. xEy if and…

A: Since you have asked question with multiple subparts so as per our guidelines we have to solve the…

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

A:

Q: Check the following relation R on the set A = {1, 2, 3, 4]} is reflexive, symmetric and or…

A:

Q: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

A: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

Q: b. Let us consider the sets A = {2,3,4,5} and B = { 0,1,2,3}. Define the relation R: A → B such that…

A:

Q: Set S= {(x, y) e R x R: y – x is an integer}. a) Prove that S is an equivalence relation on R. b)…

A:

Q: Q1. Let A be a set of nonzero integers and let be the relation on A defined by (a, b) - (c, d)…

A: Solution:-

Q: a) If R and S be two relations from set A to B. Show that (RNS)-¹ = R-¹ S-¹ b) Justify the following…

A: We know that ,  A relation R defined on a set A is called equivalence relation if R satisfies the…

Q: The relation on the set of integers R= {(x,y):5 divides x +y} is O a. none of the choices O b.…

A: Use the relevant definitions.

Q: 7b, 7c, and 7d

A:

Q: The domain for a given relation is the set of all integers. Select the correct description of the…

A: we have given a relation that  x and y are related if and only if x and y are both negative or both…

Q: Let be the relation on True False N defined by R={(n, m) : m³ = n + 1). Then R is one-to-one.

A:

Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: the 品|名 Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A b) as follows: For every (x,…

A: using the concept of relation ...

Q: R How to prove that " If is the equivalence B relation on the set and is the function R = IB then

A: given in question R is a equivalence relation on set B that means R is reflexive ,transitive  and…

Q: Prove or disprove: 1. For any relations R and S, ran(S • R) = ran(S). 2. If R and S are equivalence…

A:

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

A:

Q: equivalence

A:

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A:

Q: 9.16. Let A = {a, b, c, d}. How many relations defined on A are reflexive, symmetric and transitive…

A: given A=a,b,c,d claim- how many realations defined on A are reflexive , symmetric and transitive and…

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: Step 1:   The given relation is defined as:

Q: 8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d)…

A: Equivalence relation