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

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

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

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

A: By definition of  relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: Which of the following relations are transitive? The relations are in bold. (Remember: A relation R…

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Q: For each of the following relations ~ on sets X, determine whether it is reflexive, symmetric or…

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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: 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: Define a relation D on the set of real of numbers as follows: Vx, y ER, xD y ⇒x-y is rational…

A: Correct option is  D is reflexive , symmetric and transitive.

Q: For each relation, decide whether or not that relation is reflexive, symmetric, antisymmetric or…

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Q: Define a relation D on the set of real of numbers as follows: Vx, y ER, x Dy ⇒ x-y is rational…

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Q: d. {(0,0), (1,1), (1,3), (2,2), (2,3), (3,1), (3,2), (3,3)} е. {(0,0), (0,1), (0,2), (1,0), (1,1),…

A: Explanation of the answer is as follows

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: Let A = {0,1, 2}. Each of the statements below defines a relation R on A by (m,n) E R if the…

A: A relation between two sets is a set of ordered pairs x,y where x is an element from the first set…

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

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

Q: 1 Complete the second and third columns of the table. Where possible, complete the last column as…

A: We have a table, we have to fill in the blanks in the table.

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

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Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b), (a, c), (b, c)} To obtain the…

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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: Given the following relations on the set of real numbers, find R O S: R= {(a, b) E R² | a < b}, the…

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want any…

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: The domain of a relation R is the set of integers. x is related to y under relation R if x 2 = y.…

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

A: See the detailed hand written solution below.

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

A: Given: The number of watermelons in a truck all are weighted on a scale. The scale rounds the weight…

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: PROBLEM 4 For each relation, indicate whether the relation is: · Reflexive, anti-reflexive, or…

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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: PROBLEM 4 For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or…

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Q: The points defined by the relation x2 - y2 = 1 are symmetric across which of the following? Select…

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Q: (a) The domain of the relation L is the set of all real numbers. For r, y € R, rLy if r < y. (b) The…

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Q: Which of the following relations is an equivalence relation? [A] xRy if and only if x-y=8 [B] xRy if…

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

Q: Give an example of a relation which is (i) reflexive and transitive but not symmetric; (ii)…

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Q: A relation R is defined on the sets of integers by aRba2+b2=(a+b)2-2ab Show that R is symmetric

A: A relation is called symmetric if aRb⇔a2+b2=(a+b)2-2ab

Q: Match the ordered pairs of integers on the left with the relation they belong to on the right.

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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: Given the following relations on the set of real numbers, find R S: * R = {(a, b) E R² | a < b}, the…

A: Given: The sets are ,

Q: For each of the following relations, give the domain and range, and indicate which are…

A: Given, relation is 3, 5, 5, 7, 7, 3. Domain is the set of x values for which function is defined. In…

Q: A relation consists of the following points and the segments drawn between them. Find the domain and…

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Q: PROBLEM 4 For each relation, indicate whether the relation is: Reflexive, anti-reflexive, or neither…

A: (a) Given the domain of the relation L is the set of all real numbers. For x,y∈ℝ, xLy if x&lt;y…

Q: The domain for a given relation is the set of all integers. Select the correct description of the…

A: we have given a relation that  x and y are related if and only if x and y are both negative or both…

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

A: (a) Take x =1.

Q: Let R be the relation on the set of all mathematicians that contains the ordered pair (a, b) if and…

A: Let R be the relation on the set of all mathematicians that contains the ordered pairs  (a,b) if and…

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

A: