3. Let L be the collection of all lines in the plane. Define a relation on L by saying that two lines are equivalent if and only if they are parallel or equal. Show that this is an equivalence relation on L. 4. Define a relation on C by

Q: (b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive?…

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Q: Please do the following questions with handwritten working out

A: Step 1: Step 2: Step 3: Step 4:

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Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. I know the…

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Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: Show that “is unitarily equivalent to” is an equivalence relation on Mn×n(C).

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Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: B: Solve the following equation by Finite Differences Method, choose h = 0.25 d²y dx²-y=x+y ' y(0) =…

A: Step 1:Step 2:Step 3:Step 4: Reduced echelon form step:

Q: Proposition 2.12. Suppose- that R is an equivalence relation on a set A, and let a, b e A. Then the…

A: Given below the detailed Solution

Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is irrational OD…

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Q: "Let R be the relation defined on Z by aRb if a + b is even. Show that R is an equivalence relation…

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Q: 1. In the diagram below, there are 9 points and 8 lines: (a) Let be the relation between the points…

A: Given, In the diagram below, there are 9 points and 8 lines. a) Let ⋄ be the relation between the…

Q: Show which of each of the three properties "reflexive, symmetric, and transitive" apply to each of…

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Q: Q.1 Explain why the following statements are false 1- The relation 1 2 3 4 a 1 0.1 0.2 b 0.1 0.3 0.1…

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Q: Let S be the equivalence relation on P({1,2,3,4}) — {0} defined by XSY if and only if max(X) – |X| =…

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Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: 2. Let A = [1,3], B = {5}, and C = [4,6]. Write the inequalities (or equalities) that specify each…

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Q: Consider the following relations: R₁ = {(a, b) € R²1 a> b), the greater than relation R₂ = ((a, b) =…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Define a relation T on the set of integers as follows: rTs if and only if 4 (m-n) (4 divides m-n)…

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Q: 9. For each of the following relations on N, determine which of the five properties are satisfied.…

A: We have to determine properties based on the given relations on ℕ

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: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

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Q: Show that each of the following relations equivalence classes. on Z is an equivalence relation, and…

A: In the given question we have to find the equivalence classes.

Q: Characterize the relations in questions 14 and 15 in terms of whether each is reflexive,…

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Q: Problem 2: Relations Define he relation R on N as Ve, deN, (c, d) € R iff e+d is even. (a) Prove…

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Q: 6. Given the following relations on the set of all integers where (z,y) = R if and only if the…

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Q: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: What is the significance of the line above the 'a' variable in this context?

A: Given . is nothing but a element of A.And the set is just denoted by, is called the class of . It…

Q: Show that if for a relation R we know that R2 C R, then R transitive, and conversely. Ent. There are…

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Q: For each of the following relations, determine if they are reflexive, symmetric, antisymmetric,…

A: R = x,y|x=y R = x,y|y, y,  y∈ℝ ------------------------Reflexive: a,a exist , for every a∈R.y =…

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Q: 17. Consider the relation R = {(x,y):x-y is an integer) Which of the followings can not be element…

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Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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Q: Please do the following questions with handwritten working out.

A: Step 1:You're absolutely right! Here's the proof that the intersection of two transitive relations…