Numbers, Closures and Types of Relations

This quiz contains multiple-choice problems on relations types and closure, partial orderings and equivalence classes.

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Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here, R is known as a/an

Equivalence relation

Reflexive relation

Symmetric relation

Transitive relation

Consider the congruence 45 ≡ 3(mod 7). Find the set of equivalence class representatives from the following.

{…, 0, 7, 14, 28, …}

{…, -3, 0, 6, 21, …}

{…, 0, 4, 8, 16, …}

{…, 3, 8, 15, 21, …}

Determine the partitions of the set {3, 4, 5, 6, 7} from the following subsets.

{3,5}, {3,6,7}, {4,5,6}

{3}, {4,6}, {5}, {7}

{3,4,6}, {7}

{5,6}, {5,7}

Determine the number of equivalence classes that can be described by the set {2, 4, 5}.

125

5

16

72

Determine the number of possible relations in an antisymmetric set with 19 elements.

23585

2.02 * 1087

9.34 * 791

35893

For a, b ∈ Z, a / b means that a divides b is a relation which does not satisfy

Irreflexive and symmetric relations

Reflexive and symmetric relations

Transitive relation

Symmetric relation

For a, b ∈ R, a = b means that |x| = |y|. If [x] is an equivalence relation in R, find the equivalence relation for [17].

{,…,-11, -7, 0, 7, 11,…}

{2, 4, 9, 11, 15,…}

{-17, 17}

{5, 25, 125,…}

Which of the following is an equivalence relation on R for a, b ∈ Z?

(a - b) ∈ Z

(a^2 + c) ∈ Z

(ab + cd) / 2 ∈ Z

(2c^3) / 3 ∈ Z

Determine the set of all integers a, such that a ≡ 3 (mod 7) such that −21 ≤ x ≤ 21.

{−21, −18, −11, −4, 3, 10, 16}

{−21, −18, −11, −4, 3, 10, 17, 24}

{−24, -19, -15, 5, 0, 6, 10}

{−23, −17, −11, 0, 2, 8, 16}

Which of the following relations is the reflexive relation over the set {1, 2, 3, 4}?

{(0,0), (1,1), (2,2), (2,3)}

{(1,1), (1,2), (2,2), (3,3), (4,3), (4,4)}

{(1,1), (1,2), (2,1), (2,3), (3,4)}

{(0,1), (1,1), (2,3), (2,2), (3,4), (3,1)

Every Isomorphic graph must have a __ representation.

A cycle on n vertices is isomorphic to its complement. What is the value of n?

5 32 17 8

How many perfect matchings are there in a complete graph of 10 vertices?

60 945 756 127

What is the grade of a planar graph consisting of 8 vertices and 15 edges?

30 15 45 106

A __ is a graph with no homomorphism to any proper subgraph.

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Quiz/Test Summary
Title: Numbers, Closures and Types of Relations
Questions: 15
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