7. (Relations) Consider the set A= (1,2, 3, 4, 5), and a relation R defined by zRy -y is an integor multiple of 3. (a) List all elemeuts y for which 1Ry is true. (b) Is R reflexive? Justify. (e) Is Rsymmetrie? Justify. (d) Is Rantisymmetrie? Justify.

Q: For the relation R closure of R. {(1,2), (1,4), (3,3), (4, 1)} find (i) R2 (ii) R3 and (iii)…

A: The given relation,

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: i Determine whether or not the relation R on the set of all real numbers is reflexive, symmetric,…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: (a) Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z ×…

A:

Q: Let R = {(x, y) ∣ x ≥ y} be a relation from set A = {6} to B = {5,7}. a. List the order pairs of…

A: Given,          R=x,y/x≥y          Set A=6          Set B=5,7

Q: 8. Let S = {(a, b), (b, a), (b, d), (b, e), (b, f), (c, c), (d, e), (f,c), (f, f)} be a relation on…

A: INTRODUCTION: A set of ordered pairs is a pair of components that appear in a specific order and are…

Q: 7. (6 points) Let T be a relation defined on the set A = {1,2,3} such that T = {(1,1), (1,2), (2,2),…

A: The objective of the question is to determine whether the given relation T is reflexive, transitive,…

Q: Q4) Find the following: 1- Find the relation Z from C to X where C = {1, 2, 3, 5} and X = {4, 6, 9}.…

A: Here, C=1,2,3,5X=4,6,9

Q: 2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation…

A: A relation is a subset of Cartesian product of two sets. Therefore, every element in a relation set…

Q: What is the reflexive closure of the relation R = {(a, b) | a > b} on the set of integers? Select…

A: Reflexive Relation Definition:  A reflexive relation is the one in which every element maps to…

Q: 5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12,…

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Q: (i) Give an example of a relation S on A = {1,2, 3, 4} with S is reflexive, not symmetric and not…

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Q: 1) A={1,2,3,4} Relation R on A is R={(1,1),(2,2),(2,3),(3,2)(4,2),(4,4} a. Is R reflexive? Justify…

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Q: Below is the arrow diagram for relation S with the domain {a, b, c, d}. Define relation T to be So…

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Q: Given the relation R = {(1,2),(2,3)} on the set A = {1,2,3} . What is the minimum  number of ordered…

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Q: 9. Let X = {r1,12, 23, T4}, Y = {yı,y2, Y3}, and Z = {zı, z2}, Let R be the relation from X to Z…

A: Given: 9) X=x1, x2, x3, x4, Y=y1, y2, y3 and Z=z1, z2, z3. R=x1, z1, x2, z2, x3, z1, x3, z2 and…

Q: Consider the relation R = {(a, a), (c, a), (b, c), (d, b)} then which of the following set…

A: We need to find R3 given R=a,a,c,a,b,c,d,b Now,  R2=RοRR3=RοR2=R2οR The composition of two…

Q: How does number 1 differ than a relation? Please explain how, thank you. My teacher wants me to…

A: Relation: Let A and B be two non-empty sets. A relation R from A into B is a subset of A*B.…

Q: 1. Suppose R = {(1,1), (1, 4), (2, 1), (2, 2), (3, 2), (3, 3), (3, 4), (4, 1), (4,2), (4, 4)} be a…

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Q: Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one…

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

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Q: 1. (1 pints) Let A = {a,b,..., z} and B = {1,2,..., 10} and define f = {(c, 6), (b, 9), (b, 8), (d,…

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Q: Consider the following relations R1, R2, R3, R4 on the set [4] = {1,2, 3, 4}. Each of the relations…

A: Here we use definition of function and relation

Q: Using the relation {(1, 2), (1, 4), (3, 3), (4, 1)}, write the relations that have the minimum…

A: Relations are an essential concept in mathematics that describe the connections or associations…

Q: (a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p,p), (p, q), (q, r), (r,…

A: (a) R is a relation on the set A = {p, q, r, s}       R = {(p, p), (p, q), (q, r), (r, s), (r, r),…

Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.