2. For each of the following relations, indicate whether it is a partial order, a strict order, or an equivalence relation. Briefly justify your answers. a. Ris a relation on set {1,2,3, 4} with R = {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4, 4)}. b. Ris a relation on the set of all people such that (a, b) E R if a is taller than b.

Q: 4. Let f : X → Y define a relation on the set X by „Ry if and only if (x) = fy). Is f an equivalence…

A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: 1. This relation satisfies all the conditions of equivalence relation i.e reflexive, symmetric and…

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

A:

Q: For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, symmetric,…

A: The Reflexive Property states that for every real number x,x=x x , x=x . Symmetric Property. The…

Q: Let {2,3,4}{2,3,4} and {8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and only if…

A:

Q: Below is the Hasse diagram for a partial order relation R on the set {a, b, c, d, e}. e d be C Are…

A: Introduction: Hasse diagram is very significant in graphing a relation. In this diagram, the…

Q: {(a, b) acb, a and b are finite set of integers}

A:

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: 1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y')…

A:

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…

A:

Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

A:

Q: 11. Prove or disprove: if a relation R is transitive, then R-1 is transitive.

A:

Q: If R is a relation defined from the Set A = { 6,12,25,36} to the set B = {3,4,5,6} as follows: If R…

A: NOTE-AS WE ARE ALLOWED TO ANSWER THREE SUBPARTS IN ONE SESSION SO, I HAVE ANSWERED FIRST THREE…

Q: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

A:

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

A: A=3,4,5B=1,2,3,4R=x,y: x∈A, y∈B ∋xy&gt;7 a. R=3,3, 3,4, 3,5, 4,2, 4,3, 4,5, 5,2, 5,3, 5,4, 5,5

Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R?  Note: Select the order that…

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Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

A:

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

Q: Determine whether the given relation is an equivalent relation on {1,2,3, 4, 5}. If the relation is…

A: Equivalence class of an element a is given by [a] such that [a]={b:(a, b) lies in R}

Q: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

Q: Given the relation R- {(1,1), (2.2). (3,3).(4.4), (1,2). (2,1). (3,4), (4,3)) on the set X…

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Q: d) Let R be a relation on Z and x R y if x - y is even. e) Let R be a relation on N x N where (a, b)…

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Q: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: For each of the following sets A and binary relations ∼, decide whether ∼ defines an equivalence…

A: (a)

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

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Q: If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence…

A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

Q: 1. Consider the relation R1: R - R such that (r1, y1)R1 (X2, y2) if and only if both points are on…

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Q: 5. For each of the following relations, indicate whether the relation is reflexive, anti-reflexive,…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: For each of these relations on the set {1,2,3,4}, draw the graph of the relation: {(1,1), (2,2),…

A: For each of these relations on the set {1,2,3,4}, to draw the graph of the relation.

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

A:

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 diudes (x −…

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: 9.13. Let S = {a, b, c}. Then R= {(a,b)} is a relation on S. Which of the properties reflexive,…

A:

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

A: If R is any symmetric relation on a set A, then R-1 is symmetric.Proof :1. Let R be any symmetric…

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

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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…

Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

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Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: As per answering guideline, we can answer only one question at a time. Please repost other question…

Q: Which of the following definitions for the relation R (defined below) on A would constitute an…

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

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

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

A: Given

Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5} If the relation is…

A: To find: (i)the given relation is equivalence or not.             (ii) The equivalence class.

Q: Let A = {cat, dog, bird, rat} and R be a relation on A defined by {(r, y) : x and y have at least…

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Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5}. If the relation…

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Q: Let C = {1, 3, d, e}. Let R = {(1, 1), (1, 3), (1, e), (3, 3), (3, d), (e, 3) be a relation on C.…

A: The given set is C = {1,3,d,e} and the given relation is R={ (1,1),(1,3),(1,e),(3,3),(3,d),(e,3) }…

Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :

A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4  Consider A=1,2,3,4