What is the possible number of reflexive relations on a set of 5 elements?

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

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Q: Every equivalence relation is reflexive. True False

A: A relation is said to be an equivalence relation if and only if the relation R is reflexive,…

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

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Q: is the following relation a functic {(1, 5), (-1, 7), (1, 8), (-4,9)} yes no

A: 1, 5, -1, 7, 1, 8, -4, 9.

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: Identify the relation on set (1,2,3,4} if it is reflexive, symmetric, antisymmetric or transitive.…

A: We know that , relation is relationship between sets of values. A binary relation R defined on set A…

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

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Q: 1. List the domain and range for the relation. {(11, -5), (-10, 15), (3, 5), (7,-5)} O Range: {-5,7,…

A: Domain is the values of x and range is the values of y in ordered pairs ( x , y )

Q: The equivalence class of -2 for the relation congruence modulo 5 is о (... -11, -6, —1,4, 9, 14,…

A: Second option is correct.

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: 1. Express the following relations as a table and digraph. а. {(1,2), (1,3), (1,4), (2,1), (3,3),…

A: Relations as a table and digraph According to our guidelines,we can answer only first question.…

Q: Show that the number of equivalence relation in the set {1, 2, 3} containing(1, 2) and (2, 1) is…

A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

Q: a) How many symmetric relations on an n-element set are there? b) How many ways are there to choose…

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Q: Consider the relation R = {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)}. Is R reflexive,…

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Q: How many different functions are there from a set with 10 elements to sets with 5 elements?

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Q: In  a scout camp each girl is familiar with exactly 10 boys and each boy is familiar with exactly 10…

A: Let G be an r-regular bipartite graph, r≥1 with particle sets U and V. Then U =V .

Q: Let A = {1, 2, 3, 4, 5, 6} and R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 3), (3, 2)}.…

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Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…

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Q: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

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Q: 1), consider the relation of R= {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),(3, 3)…

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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: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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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: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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Q: What is the composite

A: Let A,B and C be three sets. Suppose that R is a relation from A to B, and S is a relation from B to…

Q: Define: what is an equivalence relation?

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Q: GIve a simple example of the Well Ordering Principle of Integers

A: We have to explain the Well Ordering Principle of Integers using an example.

Q: Give an example of a relation which is a) One-one and onto b) Many - one and onto c) One-one and…

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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: d) Determine the total number of equivalence classes.

A: Given that: View S3 as a subset of S5 in the obvious way. For σ,τ∈S5 Define σ~τ if σ~τ-1∈S3

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: What is the domain of the relation (8, 2), (6, 4), (4, 2), (2, 4)? O 2,4 O 2, 4, 6, 8 O 6, 8 O 2, 4,…

A: Concept: Domain is the set of all first elements of ordered pairs (x-coordinates).

Q: Prove or disprove if the composition of surjective relations is surjective. If it is not true, find…

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Q: The domain is {A, B, C, D, E, F, G, H}. The relation is the set: {(C, B), (D, C), (C, F), (G, H),…

A: Given domain is A, B, C, D, E, F, G, H   The relation is the set C, B, D, C, C, F, G, H, F, B, A, B,…

Q: The number of equivalence relations on the set {1, 2, 3, 4} is

A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…

Q: 2) Let A be the set of all integers. Suppose that xRy + x and y have the same reminder when divided…

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Q: Suppose there are two transitive relations R, S Disprove the claim that the composed relation S R…

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Q: b) Write out, using set notation, the equivalence class for the point (0, 2)

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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: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…

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