3. ** Prove that the relation D given by xDy iff / EZ ΕΖ (namely, xDy if x is a divisor of y), on the set Z is reflexive and transitive.

Q: 14. Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A→ B as follows: For all (x, y)…

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Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: 1. Give an example of a set S with a relation ~ on S such that ~ is symmetric and transitive but not…

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Q: The relation R defined on a set A is antisymmetric if (a, b) ER = (b, a) E R for (A) Every (a, b) ER…

A: A relation R is said to be antisymmetric if (a,b)∈R and (b,a)∈R implies a=b

Q: 2. Let D be a relation defined on Z as follows: For all x, y € Z, x D y iffx|y. Determine if D is…

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Q: Consider the relation being described by the following arrow diagram. Which of the these statements…

A: (i) It is given that ;      S = {6, 7, 8}  and  T = {2, 4, 6} And the relation between S and T is :…

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: Define a relation on Z as follows: For m, n € Z, m~n ⇒ 5|(m - n). (5.1) Prove that is an equivalence…

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Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: 8. Define a relation on Z as xRy if |x-y| < 1. Is R reflexive? Symmetric? Transitive? If a property…

A: Given, Define a relation on Z as xR y if |x-y| &lt; 1. we have to find Is R reflexive? Symmetric?…

Q: 12. Suppose that B is a nonempty set, and let A denote the set of all functions from B to B. Let F…

A: B≠ϕ    A={f f:B→B function}    F={ f f:B→B bijective}    S={(f,g)∈A×A ∃h∈F s.t f=h-1∘g∘h} a…

Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

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Q: 6. Let R be the following relation on {a, b, c, d, e}. MR = (ants) Represent R with a digraph. TULLE…

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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: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: 4. Determine which properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does…

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Q: Which of the following is/are true for the relation R, where a is related to b (aRb), if and only if…

A: Suppose, A be any set and suppose R:A-&gt;A is a relation. Then, R is reflexive: if for every x in…

Q: 1 (d) D) Write an equation for which the graph would be a vertical translation five units downward…

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Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b – a)". So for example (6,2) € R and…

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Q: Define a relation on Z by aRb if and only if a divides b. Is R an equivalnce relation? Why or why…

A: To define a relation on the set of integers Z, denoted by "aRb," where "a" divides "b," we need to…

Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: 1. Let R be a relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by R = {(a, b) ∈ A × A | 4…

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Q: 4. Define a relation R on N by aRb if a and b have no common factors except 1. (a) Give an example…

A: We have define  a relation R on natural numbers (N) by aRb if a and b have no common  factors except…

Q: Given set A = {1, 2, 3, 4}, mention 5 or more relations (R) defined on A such that R does not…

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Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b- a)". So for example (6, 2) € R and…

A:

Q: Suppose that R is a symmetric relation. Match the correct term with each blank space in the…

A: Suppose  that R is a symmetric relation than prove that R-1⊆R Proof: Suppose that &lt;x,y&gt;∈R-1.…

Q: (1) Show v is an equivalence relation on S. (2) Describe the equivalence classes of . (3) Describe…

A: Given: Define ~ on S=a, b: a, b∈ℤ, b≠0 by a, b~c, d if and only if ad-bc=0. To show: 1) ~ is an…

Q: 8. (6 points) Define a relation R on Z as follows: For all integers m and n, m R n ⇒ (m − n)is a…

A: The objective of the question is to understand the properties of the relation R defined on the set…

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

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Q: Reflexive. • Anti-reflexive. • Symmetric. • Anti-symmetric. Justify all your answers. Transitive. •…

A: Let's consider a few examples of elements inside the relation R, where (a,b)∈ R if and only if…

Q: The relation R=((a,a),(b,b)) on set X=(a,b) is. transitive symmetric reflexive anti-symmetric None…

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Q: 6.3. Let (A, <A) and (B,<B) be two partially ordered sets. One can define on the cartesian product A…

A: Given: A, ⩽A and B, ⩽B are partially ordered sets.  A Cartesian product A x B is defined with…

Q: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: (Relations) Consider the set A = {1,2, 3, 4, 5}, and a relation R defined by x Ry + x² – y is an…

A: Since you have posted a multipart question and we can answer three subparts. So, answered the first…