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This quiz contains multiple-choice problems on relations types and closure, partial orderings and equivalence classes.
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?
How many perfect matchings are there in a complete graph of 10 vertices?
What is the grade of a planar graph consisting of 8 vertices and 15 edges?
A __ is a graph with no homomorphism to any proper subgraph.
