(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: 1. Let A = {blue, yellow, red}, B = of the relations below (a) determine if it is a function (b) if…

A: R1: D X B={(cat,blue),(cat,red)} So, {(cat,blue)} ⊂{(cat,blue),(cat,red)} Therefore R1 is a…

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

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Q: The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b)…

A: Given relation is ρ =  a, b ∈ ℝ × ℝ : 1 + ab &gt; 0

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

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Q: Determine whether the following relations R from A to B is a function or not. If the relation is not…

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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: Given the relations F = {(q, p)|5p − 4q2 − 3 = 0 p, q ∈ ℝ} and                                G =…

A: Given relations are  F=q,p:5p-4q2-3=0 , p,q∈ℝ        (i)F=p,q:5p-4q2-3=0 , p,q∈ℝ        (ii) Let,…

Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

A: Solution:

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: A relation R is defined on the A={1,2,3...9.10}  as follows: xRy means "3x- 2y=1"   List the…

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

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Q: Let R be a relation on the set of all functions from Z to Z defined by: R = {(f,9)|f(1) = g(3) or…

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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: Let G be a relation from C={-1, 0, 1, 2} to C {-2,-1, 0, 1, 2} with G={(-1,0), (0,1),(1,2), (2,-1)}.…

A: Given query is to find G is a function or not.

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: Identify which of the following functions is one-to-or onto, and/or one-to-one correspondence.…

A: 5. Given: g1:ℤ→ℤ defined by g1=x,y|y=x 6. Given: g2:ℤ→ℤ+ defined by g2=x,y|y=3x+1 one to one:  f:A→B…

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: Determine whether the function f from { a, b, c, d} to { a, b, c, d} is injective (one - to - one),…

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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: True or False. Show me how you find the answer even if you get it by tossing a coin. Suppose…

A: a )  true b ) True c) True d) False e) False

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. The functions g and h are defined by g: x→x2 – 4 and f: x . where x is a 2-x real number. i.…

A: Domain or rational function of the form f(x)/g(x) is the set R- {x:g(x)=0}.

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: 5. Function fand g are defined by formulas as shown below. f(x) = x³ and g(x) = x- 1, for all real…

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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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