Problem 7. A relation is defined on the set of positive integers N by n ~ m if either n divides m or m divides n. Determine, with proof, whether is or is not: (1) reflexive (2) symmetric (3) anti-symmetric (4) transitive.

Q: Question 13 How many elements are there in the relation R on the set {0, 1, 2, 3, . . . , 100},…

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Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

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Q: 1. Suppose that we have the binary relations R1 C Ax B, R2C B×C, and R3 C C x D. Then the relations…

A: As per the question we are given that the relations : R3 o (R2 o R1) and (R3 o R2) o R1 are…

Q: Let A = {1, 2, 3}. Then show that the number of relations containing (1, 2)and (2, 3) which are…

A: The smallest reflexive relation on set A containing (1, 2) and (2, 3) is

Q: please solve this abstract algebra question for me

A: (a) True

Q: What is to be done to determine the lower class boundary of the class interval 7.5-11.5 A. Subtract…

A: Given: Class interval = 7.5 - 11.5

Q: PROBLEM1 Instruction: Prove that the relation is  an equivalence relation.  For x, y ∈ R say x is…

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Q: 1. Suppose that we have the binary relations R1 C Ax B, R2 C B×C, and R3 C C x D. Then the relations…

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Q: In the set A = {1,2, 3, 4} is defined a relation R by ? = {(1,1), (1,3), (3, 4), (4, 3)}. ndicate…

A: Given A = {1, 2, 3, 4} R = {(1, 1), (1, 3), (3, 4), (4, 3)}

Q: 1. Suppose that we have the binary relations R1 C A× B, R2 C Bx C, and R3 C C x D. Then the…

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Q: Problem 2.32. Is there an example of a space X, a subset Y C X, and a point x € X such that x is a…

A: Limit point of a set: Let X, τ be a topological space and Y be a subset of X. A point x is said to…

Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

Q: PROBLEM 30. For (x, y) and (u, v) in R2, define (x, y) ~ (u, v) if x² + y² = u? + v?. Prove that…

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Q: Problem 1. Let A and B be two non-empty sets that are bounded from above. Show: If sup A < sup B,…

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Q: Problem 12.2.8. Suppose X is an uncountable set and Y C X is countably infinite. Prove that X and X…

A: Given that X is a uncountable set and Y⊂X is a countably infinite set. To find : X and X-Y has same…

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: Please solve this problem. Thank you!

A: Note:R is a relation from A to B iff R ⊆ A×B.If R is the relation on a set A then R ⊆ A×A.And if (x,…

Q: Problem 3 Let R be the relation on the set of ordered pairs of positive integers such that ((a, b),…

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Q: Problem 3. Suppose that there is a group of n people, where n 2 2. Prove that there are at least two…

A: Let us suppose that there is 1 person who has 0 friends. If 1 more person has 0 friends then we will…

Q: A relation that assigns to each element x from a set of inputs, or ________, exactly one element y…

A: To fill: The blanks of statement: Given: The statement is "A relation that assigns to each element x…

Q: 4.4.6 Determine if the following relations are reflexive, irreflexive o ther (a) The relation x < y…

A: According to the given information it is required to check whether the relation is reflexive,…

Q: Related to the solution for exercise problem 12, in section 7.4 of textbook "Discrete Mathematics:…

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Q: Suppose that P is a unary relation symbol, Q is a binary relation symbol, f is a unary function…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: Given the relation of this table: 1|0 S 1|0|3 2 What is the rule for this relation? O 3 (n +1) 6 O 2…

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Q: y)∈R means that x²-y² is a nonnegative integer. Which of the following is true?     a. 1 R 2 b. 2 R…

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Q: 4. Given s and t, relations on Z, s = {(1,n) : n € Z} and t = {{n,1) : n E Z}, what are st and ts?…

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Q: Please solve this question. please explain thoroughly. Thanks

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Q: 1), consider the relation of R= {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),(3, 3)…

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Q: Let S be the set of integers. If a, b E S, define aRb if ab &gt;= 0. Is R anequivalence relation on…

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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: Question 6 For each of the relations on A ={1, 2, 3} below, R= {(1, 1), (1, 3), (3, 3)}, S = {(1,…

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Q: 1. Suppose that we have the binary relations R1 C Ax B, R2 C B×C, and R3 C C x D. Then the relations…

A: Use the following definitions, to obtain the solution. Let A and B be any two sets. The binary…

Q: Let's generalize the situation in problem #1. Consider the relation < on the set [n] : {1,2,...,n}.…

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Q: For each of these relations on the set {1,2,3,4}, draw the graph of the relation: {(1,1), (2,2),…

A: For each of these relations on the set {1,2,3,4}, to draw the graph of the relation.

Q: 2. Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. a)…

A: Answer :

Q: 1. Suppose that we have the binary relations R1 C A× B, R2 C Bx C, and R3 C C x D. Then the…

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Q: QUESTION 9 Let A={1,2,3,4} and the relation R={(1,1), (2,2), (3,4), (4,3), (4,4)}. Select the…

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Q: (b) Suppose that the experiment A has M mutually exclusive possible out- comes Am, and the…

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Q: 2. Consider the following relations on the set of integers: R1 = {(a, b) | a b}, R3 = {(a, b) | a =…

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Q: 3. Suppose that we have the following four tuples in a relation S with three attributes ABC:…

A: Given: Let us consider the four tuples, ABC:1,2,3,4,2,3,5,3,3,5,3,4. Let's determine the…

Q: 39. Use the following graph to evaluate a. f' (1) and b. ƒ' (6). -8-6-4-2 YA 8 6 4 2 O 2 -6 -8 2 6 8…

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Q: 1. For what values of k is the null space of A = k -1 a line?

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Q: The relation xy >= 1 where x,y are on the set of all integers is reflexive. True False

A: Given relation xy≥1, where x,y are on the set of all integers

Q: Let be the relation on True False N defined by R={(n, m) : m³ = n + 1). Then R is one-to-one.

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Q: Problem 3. Suppose that every non-empty set that is bounded from above has a supremum. Show that…

A: Result :  Let S be non-empty subset of ℝ and let -S=-x∈ℝ | x∈S ,Then S has a supremum b if and only…

Q: ave a class boundary that is less than zero?  On the probelem I am working, the class goes from 0-5

A: Class boundaries are the values which help in separating the data points in statistics.

Q: For every element x in A, there is an element in y is B such that (x,y)∈F. QUESTION: How does this…

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Q: Suppose S = {1, 2, 3} and T = {1, 2, 3, 4}. Find the sets corresponding to the binary relations s<t…

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Q: PROBLEM 3 A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be…

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