Q2. (a) Find the equivalence class [-3]5 (b) Find the ordered pairs of the relation R from the set A = B = {2,3,5}, defined by R = {(x, y): x + 3 ≤y} {0, 1,2,3} into the set

Q: The relation on the real numbers R defined by a ~ b if both a > b and b>a is not an equivalence…

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

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Q: In each item below, verify that ~ is an equivalence relation on the given set. Let S = Z × N. Define…

A: Since you have asked multiple questions, we will solve the Question Q (a) and (b) for you. If…

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: 11. Let R₁ and R₂ be the relations on {1,2,3,4} given by R₁ = {(1,1), (1,2), (3,4), (4,2)} R₂ =…

A: Sol:- To find R1 o R2, we need to compose the two relations. The composition of relations R1 and R2…

Q: Which of these relations on the set {0, 1, 2, 3} are equivalence relations? Determine the…

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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: Q4) Let S be the set of registration numbers of students enrolled in a BSCS program in a university…

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Q: 7. Let (a, b), (c,d) E R2. Define a relation ~on R² by (a, b) (c,d) if 2a - b = 2c-d. (a) Show that…

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Q: NXN set on " (a,b)~ (c,d) -) a+d -b+c %3D define d as, equiualence relation? Shaw Is reation ""

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Q: 4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an…

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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: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

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: 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: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

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Q: Let R=}(x,y)|2 divides 8x+by} be a relation the Set H= {1, 2,3.4,5, 6. 10 Determine whether the…

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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: 9. The relation ~ defined on the set of natural numbers by a ~ b means 'a – b is even is : A. an…

A: Equivalence relation : A relation which is reflexive, symmetric and transitive is an equivalence…

Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

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Q: а) The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

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Q: 9. List the ordered pairs in the equivalence relation on A = {1, 2, 3, 4, 5} associated with these…

A: Equivalence relation is relatuon which is reflexive, symmetric and transitive.

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

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: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

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