In each case determine if the given relation R on A is an equivalence relation. Justify your answer. (a) A = Z and aRb if ab ≥ 0. (b) A = Z and aRb if 5|a − b.

Q: a. Verify reflexive property on the relation R;= {(1, 1), (1, 2), (2, 2), (3, 3), (3, 4), (4, 4),…

A:

Q: Suppose that the relation T is defined as follows. T= ((-1, 4), (7, 1), (-1, -5)} Give the domain…

A:

Q: A relation Ron A is an equivalence relation if it is reflexive, symmetric, and transitive. Given: A…

A:

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: 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: 2. Which is the inverse of the relation {(-2,5), (-1,3), (0,-1), (1,-3), (2,-5), (3,-7)}? O {(5,-2),…

A: The given relation is -2,5,-1,3,0,-1,1,-3,2,-5,3,-7

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: Please choose the correct answer. Thank you If X={1, 4, 7} and Y={2, 3} and define a relation R…

A: The connection between two sets is defined by a relation. If set A has relation with set B , then…

Q: Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural…

A:

Q: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

A:

Q: 1. List the domain and range for the relation. {(11, -5), (-10, 15), (3, 5), (7,-5)} O Range: {-5,7,…

A: Domain is the values of x and range is the values of y in ordered pairs ( x , y )

Q: The domain for the relation R is Z × Z. (a,b) R (c,d) if and only if a <c and b< d. Indicate whether…

A:

Q: Let A ={1, 2}, B = {1, 2, 3} define a relation R from A to B given any {x, y} ϵ A cross B.…

A: A=1, 2, B=1, 2, 3 R is a relation defined as R=x, y: x+y2 is an integer.

Q: 10.3. Let A be a nonempty set. If Ris a relation from A to A that is both an equivalence relation…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A:

Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a&gt;c or a=c and b≥d Show…

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: 7. Identify the domain of the set (5, 3), (0,-4), (2, 5), (11, 3) and tell if the relation is a…

A: We have to identified the domain of the set  (5,3),(0,-4),(2,5),(11,3)

Q: What is the domain of the relation x(x-3) ? {(X,y): y = (x+4)(x-7)). ) {x: x = R, x -4, x > 7} ) {x:…

A: Domain of function f(x) is the set of value of x for which f(x) is defined.

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

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…

A:

Q: binary relation R is defined on the set of real numbers by xRy ⇔ lx - yl ≤ 1. Determine whether or…

A: R is not an equivalence relation. Because, R is not transitive. The Counter example is as follows…

Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

Q: 2 Use the space below to draw the so-called arrow diagrams for three functions that are 1) injective…

A: I] The arrow diagram for the function which is injective but not surjective.

Q: Q2. (a) Find the equivalence class [-3]5 (b) Find the ordered pairs of the relation R from the set A…

A: We have to answer the following questions :  (a) Find the equivalence class  -35 (b) Find the…

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

A:

Q: Definition. FractionalPart[x] takes all digits to the right of the decimal point and drops the…

A: Fractional function / Fractional partA function f:R →0 1  denoted by f(x) =xare defined by f(x) =x =…

Q: A relation consists of all the points in the x-y plane that are either on the line y=1 or the line…

A: Here, the objective is to determine if equation represent a function.

Q: For every element r in A, there is an element y in B such that (x, y) is in F. Can you please…

A: Relation: The relation from a set A to a set B is a subset of Cartesian product A×B. Function: The…

Q: Question 13 For each relation: (1) antisymmetric, and transitive (for transitivity just show two…

A: (1) Given that R=a,a,b,b,c,c,a,b,a,c,c,a,b,c,c,d Let A=a,b,c,d Reflexive relation:- A relation R on…

Q: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: MULTIPLE SELECT: Select THREE tables that represent a relation with a domain of {-2, 3, 7}. y 6 -2 O…

A:

Q: equivalence relation

A:

Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: 1) Let R be a relation on N × N where (a, b) R (c, d) if a ≤ c and b ≥ d

A:

Q: 1. List the domain and range for the relation. {(11, –5), (–10, 15), (3, 5), (7,–5)} O Range: {-5,…

A: according to Bartleby guidelines I am expected to solve only the first question. Kindly repost the…

Q: There are 3 parts to this question. The answer choices for each are all. 1) reflexive 2) irreflexive…

A:

Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…

Q: Define: what is an equivalence relation?

A:

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

A: As per answering guideline, we can answer only one question at a time. Please repost other question…

Q: O constant domain derivatives O function

A:

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

A: Given problem is :

Q: 5. Find three relation from {1, 2} to {6, 7} that are NOT functions.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: cercise 2. Give an example of a relation R on A = {1,2,3} that is neither reflexive or irreflexive.

A: Given A = {1, 2, 3}

Q: 11. List the domain and rage for the relation. 4 -6 13 O Range: { 4, 2, 6, 7} O Domain: { 4,2,6, 7}…

A: Please refer the attached image for complete Solution.

Q: Answer All Questions Please.

A:

Q: Consider a relation R on Z = {3,4,5,6} is defined by pRq iff 2p + q is even. a) Please list the…

A:

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…

Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5}. If the relation…

A: