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 divides (x – y). 1. List all the ordered pairs in the relation R? 2. Draw the directed graph of the relation R? 3. Determine whether the relation R is an equivalence relation?

Q: Let A={3,4,6,7}, and define a relation R on A as follows: For every x, y belong to A, xR y x|y.…

A: We first write elements of R then we form diagraph and then we write the corresponding adjacency…

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: Let A = (a, b, c) and R = ((a, a), (b, b), (c, c), (c, b), (b, c)). Which of the following statement…

A: Given set is  A = {a, b, c} and  R = {(a,a), (b,b), (c,c), (c,b), (b,c)} is relation on A

Q: Show that the relation R on a set A is symmetric if and only if R = R-, where R is the inverse…

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Q: 2,3,4,5

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Q: 3. a. If R is a relation defined from the Set A = { 6,12,25,36} to the set B = {3,4,5,6} as follows:…

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Q: Assume the relation R over the set {0,1,2,3,4,5,6,7,8,9} where (a,b) ∈ R if and only if
 a+b < 10.…

A: Since multiple subparts are asked, answering only the first 3 subparts. id aRb=bRa realtion is…

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: Define a relation R, on the set A = (0, 1, 2, 3) as follows. R, = {(0, 0), (0, 1), (1, 1), (1, 2),…

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Q: Let A = {3,4,5,6} and B = {1,2,3} and define a relation R: A → B as follows: For all (x, y) ∈ A × B,…

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Q: Let a relation ∼ on R2 = {(a, b): a, b ∈ R} be defined as: (a, b) ∼ (c, d) if and only if | a | + |…

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Q: Let A = {n| 3 < n S 30} and define a relation on A such that aRb iff a |b. List the relation set R.…

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Q: 8. Define a relation R on the set J = {0, 1,3,4,5,6} as follows: For all x, y EJ, x Ry ⇒ 4x² + y².…

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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: 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…

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Q: Let {2,3,4}{2,3,4} and {8,9,10}{8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and…

A: Given that:                      A={2,3,4}B={8,9,10}H is an relation from A to B such that: (x, y)∈H…

Q: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

Q: A = {1, 3} and B = {2, 4, 6}. Define a relation R from A to B as follows: for all (x, y) ∈ A × B…

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Q: Let A={1,2,3,4} and R a relation on A such that A/R={{1},{2},{3,4}}. Then the number of ordered…

A: Given problem is : Let A={1,2,3,4} and R a relation on A such that A/R={{1},{2},{3,4}}. Then the…

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: In mathematics, a homogeneous binary relation R on a set X is reflexive if it relates every element…

Q: Let S {(a,b): a,be R, a 0}. Show that the relation R defined on S by (a, b) R(c,d) if = ad be is an…

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Q: Let A= {2, 4} and B = {2, 4, 6} and define a relation R for A to B as follows: Which ordered pairs…

A: A=2,4 and B=2,4,6a,b element A×B, a,b∈R means that a+b is an integer

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

Q: Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where: ? = {(1,1),…

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Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: We have: The relation is: R=a,c,b,a,c,d,d,b

Q: 6. Let A {1,2, 3, 4, 5} and define a relation on A as follows: For all x, y E A, %3D xRy + x+ y is…

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Q: Let A 1, 2} and B = {1, 2, 3} and define a relation R from A to B as follows: Given any (x, y) E A x…

A: Given

Q: 1. Consider the relation R1: R - R such that (r1, y1)R1 (X2, y2) if and only if both points are on…

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Q: Which of the following relations is an equivalence relation? [A] xRy if and only if x-y=8 [B] xRy if…

A: We have to find which relation is equivalence relation.

Q: Let {2,3,4} {2,3,4} and {8,9,10} {8,9,10}. Define a relation H from A to B such that (x,y)∈H(x,y)∈H…

A: Given A={2,3,4} B={8,9,10}

Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: Suppose that the relation T is defined as follows. T = {(2,b), (7,0), (4,2), (7,a)} Give the…

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Q: equivalence relation

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Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows:  x1,y1≺x2,y2 if and only if x1&lt;x2 or x1=x2 and y1≤y2

Q: A relation R is called circular if (a, b) E R and (b, c) e R implies that (c, a) e R. Show that a…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve the…

Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

Q: 9.13. Let S = {a, b, c}. Then R= {(a,b)} is a relation on S. Which of the properties reflexive,…

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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 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.

Q: Let E =(1, 2, 3} and F = {-2, -1, 0} and define a relation T from E to F as follows: For all (x, y)…

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Q: Let A={5,6,7,8,9,10,11} and define a relation S on A as follows xS y 3|(x-y) (a) Is 5S7? Why? (b) Is…

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Q: The domain for the relation A is the set {2, 5, 7, 8, 11}. For x, y in the domain, xAy if |x-y| is…

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Q: given the relation R define = (0,0), (0, 1), (0, 3), (1, 1), (1,0), (2, 3), (3, 3) on the set A = 0,…

A: Given that  R=0,0,0,1,0.3,1,1,1,0,2,3,3,3A=0,1,2,3 To draw the directed graph and determine whether…

Q: 3. Find all ordered pairs in the relation R from A = (a,b) E R if and only if a + b = 9. {0,2,4,7}…

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Q: Let A = {6, 8, 10, 15, 17} and B = {2, 3, 4, 5} and define a relation R: A → B as follows: For all…

A: Given   A = {6, 8, 10, 15, 17};  B = {2, 3, 4, 5}; relation R: A → B  ordered pairs of A and B that…

Q: Let A= {5,6,7,8,9,10} and define a relation S on A as follows xSy 2|(x-y) (a) Is 5S6? Why? (b) Is…

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Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…

A: Explanation of the answer is as follows

Q: Let A = {cat, dog, bird, rat} and R be a relation on A defined by {(r, y) : x and y have at least…

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Q: Consider the relation R on the set Z defined by a R b if and only if 3|(a+2b) for a, b ∈ Z. Show…

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Q: On P2, define a relation p(x) ~ q(x) if p(0) = q(0). (a) Show that this is an equivalence relation…

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