For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither • Symmetric, anti-symmetric, or neither Transitive or not transitive ustify your answer. (a) The domain of the relation L is the set of all real numbers. For z, y € R, ILy if 1 < y. (b) The domain of the relation A is the set of all real numbers. IÂy if |r-y| <2 (c) The domain of the relation Z is the set of all real numbers. xZy if y = 2r

Q: Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 +…

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Q: The domain of the relation A is the set of all real numbers. zAy if (r-y| ≤2

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Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

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Q: R1 = {(a, b) ∈ R2 ∣ a > b}, the greater than relation R2 = {(a, b) ∈ R2 ∣ a ≥ b}, the greater than…

A: That's easy. Have a great day!!!

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

A: The given relation R is as follows. R=x,y∈Z×Z:x is a multiple of y If x,y∈R, we denote x related to…

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Q: Which of the following relations is transitive? Define a relation R in the natural number. Select…

A: We have to find

Q: If R is reflexive, symmetric and transitive then the relation is said to be--------

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Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: The domain for the relation R is Z × Z. (a,b) R (c,d) if and only if a <c and b< d. Indicate whether…

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Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

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Q: For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

A: a)  Given Domain of Relation L is set of all real numbers and for x,y∈R, xLy if x&lt;y     (i) For…

Q: For each relation F, indicate if it is: reflexive, anti-reflexive, or neither; symmetric, anti-…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: - whether the following relation is a functio- x² – 2x + 1

A: We have to identify  the given  relation is function  not

Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

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Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

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Q: The domain of the relation L is the set of all real numbers. For x, y e R, rLy if r < y.

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Q: Let R be the relation, {(a, b) e N x N:a + b is odd}. Give an example that shows that R is not…

A: Given R be the relation, {(a, b) ∈ N x N:a + b is odd}.  We find an example that shows that R is not…

Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

A: See the detailed hand written solution below.

Q: For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

A: To find- For each relation, indicate whether the relation is: Reflexive, anti-reflexive, or neither…

Q: For each relation, indicate whether the relation is: \ item Reflexive, anti-reflexive, or neither \…

A: (a) From the given data the relation is xLy if x&lt;y. (i)For every x∈ℝ,  since x is not less than x…

Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

A: (a) Let the set A=set of all watermelons in the truck and R be the relation on A, i.e R⊂A×A defined…

Q: x R y in R if x- y < 3 |

A: Note that for any real number x, |x-x|=0&lt;3.  Thus, xRx or the given relation is reflexive.

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A: We have to find which relation is equivalence relation.

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Q: Let R= {(x, y) ∣ x ≥ y} be a relation from set A = {The set of even numbers involve in user ID  to B…

A: Given, R=x,y/x≥y Let A = {The set of even numbers involve in user Id}      B = {The set of prime…

Q: equivalence relation

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Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

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Q: A relation R is called circular if (a, b) E R and (b, c) e R implies that (c, a) e R. Show that a…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve the…

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A: Definitions of symmetric, reflexive,transitive are given.We have to check them .

Q: (d) Justifying your answer, find the smallest set of related pairs which must be added to R in order…

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A: Reflexive relation: A relation R is reflexive over element X if every element X is related to…

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A: We have to determine whether the given relation is equivalence relation or not.

Q: Define a relation ~ on the set of real numbers by X~ y means | x |+|y|=|x+y|. Determine whether - is…

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Q: (c) The domain of the relation Z is the set of all real numbers. xZy if y = 2x

A: The relation Z is the set of all real numbers. xZy if y=2x. Z=x,y|y=2x (a)The relation R on set A is…

Q: Define a relation on Z x Z, xRy, |x - y| < 1. Is R reflexive, symmetric, and/or transitive? Explain…

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Q: Show that if for a relation R we know that R^2 ⊆ R, then R is transitive, and conversely.

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Q: Decide whether the following relations is an equivalence relation or not. {(x, y) | xy > 0, x and y…

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

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Q: For universe S = R², define relation ~= as: (a,b) ~= (c,d) < 2a - b = 2c - d Prove that ~= is an…

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Q: 1. Consider the relation R1 : R2 - R² such that (r1, y1)R1 (x2, y2) if and only if both points are…

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

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Q: For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

A: (a) Take x =1.

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

A: Step 1:   The given relation is defined as:

Q: Give an example of a relation. Which is(i) Symmetric but neither reflexive nor transitive.(ii)…

A: i. Symmetric but neither reflexive nor transitive.

Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

A: