(1) Define relation R on the real numbers, R, by xRy if and only if [x] = [y]. Determine which of the following properties the relation has (or doesn't have). If R has the property, prove it. If it doesn't, give a counterexample to demonstrate. • reflexive or/nor antireflexive • symmetric or/nor antisymmetric • transitive

Q: If A = {1,2,3,4} give an example of a relation R on A that is: Reflexive and symmetric but not…

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Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1A and fh = 1B. Prove…

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Q: Consider the relation R on the set of functions defined by (f, g) = R if and only if f(x) is…

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Q: Do question 3 only

A: Step 1: Step 2: Step 3: Step 4:

Q: Do question 1 only

A: For any query with the solution, please ask in the comment box.

Q: Let R be a relation over the positive integers defined as follows: R = {(a,b) | 2b < a < 3b }…

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Q: Determine whether the relation R on the set of all real numbers is reflexive, symmetric,…

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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: Define the following relations on A = {5,6,7,9). Answer each of the following questions by listing…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: Define the following relations on A = {2, 4, 5, 7}. Answer each of the following questions by…

A: According to the Bartleby guidelines,I solve first three subparts only and repost the remaining.

Q: Determine whether the relation R on the set of all real numbers is reflexive, symmetric,…

A: Consider the relation  for  Reflexive: For   Thus,  is not reflexive. Symmetric: For  but…

Q: Three relations are defined below. Decide whether each of these relations is reflexive, symmetric…

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Q: Let R be the relation on Z given by R= {(a,b) : a < b}. %3D (a) Find R-1. (b) Find R which is Z x Z…

A: relation on Z.

Q: Let A = {2, 3, 4, 5} and B = {6, 8, 10}. A relation R is defined from A to B by a R b if a | b and…

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Q: Define a relation R on Z as follows: For all integers m and n, 51(m² - n²). mRn (a) Is 1 R (-4)? Yes…

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Q: Which of the following relations are functions of y in terms of x? 1) 2) 3) 4) 5- 5+ 5+ 4- 3- 2- 2-…

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Q: Draw the diagraph of the relation R, where the relation R on {1,2,3,4} defined by (x,y) ∊ R if x^2…

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Q: Define the relation R over integers as follows: R = { (a, b) | |a - b| < 5 } Determine if R is (a)…

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Q: b) Prove or disprove: i. [x]-[x]. ii. For all positive real numbers x and y, [xy] ≤ [x] - [y].

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Q: Consider the relation R = {(1,1);(2,3);(3,5);(4,7)}. a. Prove that R is a function from {1,2,3,4}…

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Q: Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric,…

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