An ordering on a set F is a relation, represented by ≤, with the following three properties:(o1) For arbitrary x, y ∈ F, at least one of the statements x ≤ y or y ≤ x istrue.(o2) If x ≤ y and y ≤ x, then x = y.(o3) If x ≤ y and y ≤ z, then x ≤ z.

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

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Q: Let T be an irreflexive relation on the set M, then the ToT relation is also irreflexive on the set…

A: Let M=ℕ. Define relation T on M as, T=a,b : a≠ b Clearly a,a∉T for any a∈M. Hence T is irreflexive.

Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

A: According to the given information, Let S be the set of all cars sold in the period 2015 to 2020.…

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

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Q: a)Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z × Z,…

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Q: 5. Identify each relation as linear, quadratic, or exponential. a) YA b) c) -4 -20 +2 -6 4 4 6 2 YA…

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Q: Suppose that R is the relation that is represented by the following digraph ... a O True O False b d…

A: The objective is to determine whether the directed graph with the relation is a partial order or…

Q: • f(x, y, z)= . near the point (1, 1,0).

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

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Q: Show which of each of the three properties "reflexive, symmetric, and transitive" apply to each of…

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Q: Let R = { ( a, b ), ( a, d ), ( b, d ), ( c, a ), ( c, c ), ( d, b ), ( d, c ) } be a relation on…

A: Given: R=a,b,a,d,b,d,c,a,c,c,d,b,d,c   The relation R2 contains all ordered pairs (x, z) if (x, y)…

Q: Consider the following relations: R₁ = {(a, b) € R²1 a> b), the greater than relation R₂ = ((a, b) =…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Given the sets C = {1, -3} and D = {2, 3, 6}, find all ordered pairs (x,y)and those that satisfy the…

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Q: set {(a,b),(a, a), (c, a), (b, b)} (a). Let X = {a,b,c} be sets. is a relation on X and find its…

A: Answer and explanation is given below..

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: lation. Justify why your answers are corre R is a relation on the set of all people sue R is a…

A: EQUIVALENCE RELATION: If a relation R on a set A satisfies the following three criteria, it is…

Q: For non empty binary relation R={(a, a).(a, b).(a, e).(b, b).(b, e).(c, C).(c, d).(d, d).(e, e)} on…

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Q: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Let A and B be any two sets. A binary relation from A to B is i. CAXB ii. SANB CAUB Non of these…

A: Firstly we define binary relation from set A to set B, and then conclude the answer.

Q: How many relations are the

A: Given : The set is { 1, 2} .

Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

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Q: Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not…

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Q: 2. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and suppose R is a relation defined by a is related to b…

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Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

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Q: Given the relation R on the set of all integers defined by the rule (x, y) ER if and only if x 2 y².…

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Q: f d a h с 6.0 g e b

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Q: Prove or disprove: If a relation is symmetric and transitive, then it is also reflexive

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Q: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

A: Given a relation, aRb⇔ab≤0. To check whether R is an equivalence relation on set ℤ. A relation is an…