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• For a, b ∈ R define a = b to mean that |x| = |y|. If [x] is an equivalence relation in R. Find the equivalence relation for [17].(a) {,…,-11, -7, 0, 7, 11,…}(b) {2, 4, 9, 11, 15,…}(c) {-17, 17}(d) {5, 25, 125,…}This question was posed to me during an interview.Question is from Relations in section Relations of Discrete Mathematics
• Determine the set of all integers a such that a ≡ 3 (mod 7) such that −21 ≤ x ≤ 21.(a) {−21, −18, −11, −4, 3, 10, 16}(b) {−21, −18, −11, −4, 3, 10, 17, 24}(c) {−24, -19, -15, 5, 0, 6, 10}(d) {−23, −17, −11, 0, 2, 8, 16}I have been asked this question at a job interview.I would like to ask this question from Relations in chapter Relations of Discrete Mathematics
• Determine the number of possible relations in an antisymmetric set with 19 elements.(a) 23585(b) 2.02 * 10^87(c) 9.34 * 7^91(d) 35893The question was asked during an online exam.The above asked question is from Relations in chapter Relations of Discrete Mathematics
• Determine the number of equivalence classes that can be described by the set {2, 4, 5}.(a) 125(b) 5(c) 16(d) 72This question was posed to me in an online quiz.I want to ask this question from Relations in division Relations of Discrete Mathematics
• Let A and B be two non-empty relations on a set S. Which of the following statements is false?(a) A and B are transitive ⇒ A∩B is transitive(b) A and B are symmetric ⇒ A∪B is symmetric(c) A and B are transitive ⇒ A∪B is not transitive(d) A and B are reflexive ⇒ A∩B is reflexiveI got this question in an online interview.I'm obligated to ask this question of Types of Relations topic in section Relations of Discrete Mathematics
• The time complexity of computing the transitive closure of a binary relation on a set of n elements should be ________(a) O(n)(b) O(logn)(c) O(n^(n+(3/2)))(d) O(n^3)The question was asked by my school teacher while I was bunking the class.I'd like to ask this question from Types of Relations in division Relations of Discrete Mathematics
• The rank of smallest equivalence relation on a set with 12 distinct elements is _______(a) 12(b) 144(c) 136(d) 79The question was asked in an international level competition.This intriguing question originated from Number of Relations in chapter Relations of Discrete Mathematics
• How many elements are there in the smallest equivalence relation on a set with 8 elements?(a) 10^2(b) 8(c) 48(d) 32This question was posed to me in an interview for job.I would like to ask this question from Number of Relations topic in division Relations of Discrete Mathematics
• Which of the following is an equivalence relation on R, for a, b ∈ Z?(a) (a-b) ∈ Z(b) (a^2+c) ∈ Z(c) (ab+cd)/2 ∈ Z(d) (2c^3)/3 ∈ ZThe question was posed to me in an online quiz.The above asked question is from Relations topic in section Relations of Discrete Mathematics
• For a, b ∈ Z define a | b to mean that a divides b is a relation which does not satisfy ___________(a) irreflexive and symmetric relation(b) reflexive relation and symmetric relation(c) transitive relation(d) symmetric relationI had been asked this question in homework.This intriguing question comes from Relations in section Relations of Discrete Mathematics