consider the relation R on R, where R = {(a, b) | a ≤ b+1}. (a) Is the relation R reflexive, antireflexive, symmetric, antisymmetric, and/or transitive? Can you explain why? (b) Is R a partial order, a graph, an equivalence relation, or none of the above? Briefly explain.

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: If R ={ (1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} is a relation on {1, 2, 3, 4}. Find the reflexive…

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Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

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Q: (b) Define Equivalence Relation with an example. Give an example of a relation which is not…

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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: Define the relation R = {(a.b): a + b < ab} = A x B with A = {1,2,4} and B = {2,5,6). List all the…

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Q: Consider the relation R on R, where R = {(a, b) | ab ≥ 0} . (a) Is the relation R reflexive,…

A: is a relation on

Q: 4 1) 3 bes this digraph illustrate a relation that is symmetric or transitive or neither? ymmetrid…

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Q: The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b)…

A: Given relation is ρ =  a, b ∈ ℝ × ℝ : 1 + ab &gt; 0

Q: (i) Give an example of a relation S on A = {1,2, 3, 4} with S is reflexive, not symmetric and not…

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Q: 7. (Relations) Consider the set A= (1,2, 3, 4, 5), and a relation R defined by zRy -y is an integor…

A: Given, A = 1, 2, 3, 4, 5xRy ⇔x2-y is an integer multiple of 3.

Q: ii. Determine whether the relation, R = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} is: Yes/No…

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Q: Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where ? = {(1,1),…

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Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

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Q: Which is not an element of the domain in the relation below? {(-4, 6), (0, 3), (2, 2), (7, – 1)} O 2…

A: Consider the given relation in ordered pairs. -4,6,0,3,2,2,7,-1 The objective of the problem is to…

Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by R = {(1,1), (2,2), (2,4), (2,5),…

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Q: Suppose that the relation R is reflexive. Show that R* is reflexive.

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Q: Consider the relation R on R given by R = {(a, b) | a−b > 3 or a−b = 0}. (a) Show that R is not an…

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Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.

Q: Let R be the relation, {(a, b) Nx N: a + b² is divisible by 3} Give an example that shows that R is…

A: Symmetric Relation: A relation R is said to be symmetric if

Q: domain of a relation

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Q: Determine whether the following relation is an equivalence relation or not. (a) G = {(x, y) |æ…

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

Q: (a) Write a set of ordered pairs (x, y) that defines the relation.

A: Let us denote Boise=B, Miami=M, Springfield=S, Bermimgham=Br and variable for them be x. Their…

Q: Consider the following relation. R₁ = {(a, b)|2a = b or 2b = a} R₂ = {(a, b)| 4a + b b} R₁ = {(a,b)…

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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: cercise 2. Give an example of a relation R on A = {1,2,3} that is neither reflexive or irreflexive.

A: Given A = {1, 2, 3}