Consider the set Q = Z × (Z 10), and the relation fupon Q Defined as: (a, b) ↑ (c, d) + a•d = b•c a) Show that fis an equivalence relation on Q.

Q: B 4a X A 66° 20

A: The given figure is -  We have to find the value of 'x'.

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

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Q: 5. Identify each relation as linear, quadratic, or exponential. a) YA b) c) -4 -20 +2 -6 4 4 6 2 YA…

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Q: Select all pairs in the reflexive closure of the relation R, defined on the set A = { a, b, c, d }…

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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: 2 Explain why the relation on N defined as is not an equivalence relation. {(x,y): +y is a multiple…

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

A: To find the composition of two relations R and S . the domain of S°R will be same as domain of R…

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: 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: 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: 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: 3. On the relation R on the set {1, 2, 3, 4, 5} defined by the rule (x, y) e R if x+y<6. a) List the…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

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: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

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Q: R={(0,4), (3,0), (3,1), (4,2)}. Find transitive closer of R. Show diagram. A=Z+ x Z+ show relation R…

A: The question involves finding the transitive closure of a relation R and demonstrating the relation…

Q: 11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following:…

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Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

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Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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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: 3. For universe S = R² define relation ~ as: (a, b) ~ (c,d) ⇒ 2a-b2c - d. Prove that is an…

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Q: Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3,…

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Q: 3. Let X be a set and S and R equivalence relations on X. Prove or give a concrete counter example…

A: Since you have asked multiple questions, we will solve the first and second question for you. If you…

Q: Define: what is an equivalence relation?

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Q: 6. Consider the set R2 and relation~: (1, 1)~ (2, 2) if and only if x2 = ₁ + m and y2 = ₁ +n for…

A: We shall solve only the first and second part of the question. If you want to solve the remaining…