Considering A as a set which contains the elements (2,3,4,5,6,7,8}, Define a relation R from A to A by R={(xy): y is multiple of x and x#y} [Multiple means "a number that may be divided by another a certain number of times without a remainder. Example: "15, 20, are multiples of 5" a. Write R b. Depict this relation R using an arrow diagram. c. Write the matrix representation for R. d. Check whether R is reflexive, symmetric, antisymmetric.

Q: Let A = {3,4,5,6,7,8} and define a relation R on A as follows: For every x, y E A, x R y + 2|(x –…

A: The arrows between two numbers or the number and itself must differ by a multiple of 2 ie, 0,2,4,6,8…

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?.…

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

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Q: 10. What is the domain of the relation shown below? (1) {0, 1, 4} (2) {-2, –1, 0, 1, 2} {(4, 2).(1,…

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Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

Q: Given set B as B = {0,1,2,3,4}. Suppose set A is the relation and defined as a. A = {(x, y) E Z | xy…

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Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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Q: A playground consists of several structures, some of which are connected by bridges. The ground is…

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Q: 2. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and suppose R is a relation defined by a is related to b…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: (a) Write A = {10,20,30,40, ...} in the set-builder form. (b) If R be a relation on set of real…

A: Given A={10, 20,30, 40, 50.....}

Q: 7. (Relations) Consider the set A = (1,2,3, 4, 5}, and a relation R defined by zRy + 2-y is an…

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: Write a full soultion 1. Consider the following relation: {(-2,3), (1,0), (4, -1), (0, -3), (1,1)}…

A: The domain of given relation are the points which are on x-coordinate.

Q: Let A = {2, 3, 4, 6, 7, 9} and define a relation R on A as follows: For all x, y e A , x R y = 3…

A: Given A = {2,3,4,6,7,9} xRy ⇔ 3 divides (x-y) Therefore 1)  R = (2,2) , (3,3) , (4,4) , (6,6) ,…

Q: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2} and define a relation R on A as follows: For all m, n E A,…

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Q: Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4),(1, 3),…

A: The given set and the relation R is shown below.

Q: 2. Let R be the relation on the set A = (1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) e R if the…

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Q: Recall that, for any set A, the power set of A, P ( A ), is the set of all subsets of A. Consider…

A: To  find if the inclusion relation on P(A) has the properties of reflexivity, symmetry and…

Q: Let A = {x: x is a course offered by Trinity University of Asia} B = {x: x is a college in Trinity…

A: Given: A={x: x is a course offered by Trinity university of Asia} B={x: x is a college in Trinity…

Q: Let A = {0,1, 2}. Each of the statements below defines a relation R on A by (m,n) E R if the…

A: A relation between two sets is a set of ordered pairs x,y where x is an element from the first set…

Q: )Determine the power set of the set A={q,p,x}. 2)Let the relation R be {(1,2), (2,9), (5,6)}. Is R…

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Q: on A as follows: For all m, n ∈ A, m R n ⇔ 5|(m2 − n2). It is a fact that R is an equivalence…

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Q: Let A = {1,2, 3, 6}. Define a relation R on A as follows: x Ry if y – x > 0 Write out the relation R…

A: We have to find the relation and write as set notation.

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

A: Equivalence class of an element a is given by [a] such that [a]={b:(a, b) lies in R}

Q: 5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1,…

A: Let R be the relation on the set 1 , 2 , 3 , 4 , 5 containing the ordered pairs  1 , 1 , 1 , 2 , 1 ,…

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: A = {1, 2, 3} and B = {a, b}. Write a function from B to A. (d) Let R be the relation not equal…

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Q: Let A = {5, 6, 7, 8, 9, 10} Let R be a relation on A defined by R = {(a, b) : a e A, be A, Ja -…

A: Given,          Let A= 5,6,7,8,9,10  .           Let R be a relation on A defined by R=a,b :…

Q: equivalence relation

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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: Solution:   This is an equivalence relation since:A U Y = A U YA U Y = B U Y implies that B U Y = A…

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: 10. What is the domain of the relation shown below? {(4, 2),(1, 1).(0, 0),.(1, –1),(4, –2)} (3) {-2,…

A: Given relation is : 4,2,1,1,0,0,1,-1,4,-2 To find the domain of the given relation.

Q: 2. Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) eR if the…

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Q: 1 Let A be the set of all integers = {...,-3,-2,-1,0,1,2,3,...}. Define the relation R on A as…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Let A = { 1, 2, 3, 4 } and B = { 4, 6, 8, 10 }.Define a relation H from A x B as: For all (x, y) ∈ A…

A: Please see the below picture for detailed solution.

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…

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Q: Let A = {1,2,3, 6}. Define a relation R on A as follows: %3D xRy if y – x > 0 Write out the relation…

A: We have to find the relation R.

Q: Let R be the reltions R = (refer to image).

A: Consider the provided question,

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

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Q: 10. What is the domain of the relation shown below? (1) {0, 1, 4} (2) {-2, –1, 0, 1, 2} {(4, 2),(1,…

A: domin of given relation is option a is correct.

Q: Let a, be the set {0, 2, 12} Let a, be the set {4,5, 10} Let az be the set {6,9, 14} Let az be the…

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Q: Show that the relation R is an equivalence relation in the set A = { 1, 2, 3, 4, 5 } given by the…

A: Given- Set A={1,2,3,,4,5}. To Show- That the relation R is an equivalence relation in the set A = {…

Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider…

A: Given that, The relation is “same age” and the set is cars made in 2015, 2016,2017, 2018, 2019, and…

Q: Let A = {1, 3, 4, 6, 8, 9} and a relation on A is defined by the following: a R b if and only if a…

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Q: Here are two relations defined on the set {a, b, c, d}: S = { (a, b), (a, c), (c, d), (c, a) } R =…

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Q: Let A = {1,2,3,4} and B = {A,B, C, D, E}. Consider the following relations and state whether…

A: A relation will be function if for each x∈A  there exists a unique b∈B with (a, b) ∈ f. In other…

Q: Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3} and define a relation R on A as follows: For all m, n e A,…

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

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Q: 9.12. Let S = {a, b, c}. Then R = {(a, a), (a, b) , (a, c)} is a relation on S. Which of the…

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