For a modulus n > 1, consider the relation on Z where two integers x and y are considered kn for some integer k, in which case we will write x = y(_mod_n) related whenever * - y = Select all that apply: This relation is reflexive since every integer is related to itself. This relation is symmetric since if x is related to y then y is related to x. This relation is transitive since if x is related to y and y related to z then x is related to z This relation is an equivalence relation because it is reflexive, symmetric, and transitive. This relation forms a partition of the integers into n equivalence classes. Each equivalence class contains related elements, each pair of which differs by a multiple of n Each class can be represented by one of the possible remainders when dividing an integer by n. We may perform arithmetic on the classes, similar to how we may perform arithmetic with a clock.

For a modulus n > 1, consider the relation on Z where two integers x and y are considered kn for some integer k, in which case we will write x = y(_mod_n) related whenever * - y = Select all that apply: This relation is reflexive since every integer is related to itself. This relation is symmetric since if x is related to y then y is related to x. This relation is transitive since if x is related to y and y related to z then x is related to z This relation is an equivalence relation because it is reflexive, symmetric, and transitive. This relation forms a partition of the integers into n equivalence classes. Each equivalence class contains related elements, each pair of which differs by a multiple of n Each class can be represented by one of the possible remainders when dividing an integer by n. We may perform arithmetic on the classes, similar to how we may perform arithmetic with a clock.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

PLEASE TYPE ONLY**** ANSWER ALL THREE QUESTIONS Exercise 8.1.4: Arrow diagrams for relations on small finite sets. Draw the arrow diagram for each relation. (b) The domain of relation P is {2, 4, 8, 16, 32, 64}. For x, y in the domain, xPy if there is a positive integer n such that xn = y. (c) The domain of relation D is {2, 3, 12, 16, 27, 48}. For x, y in the domain, xDy if y is an integer multiple of x. (d) The domain for the relation A is the set {2, 5, 7, 8, 11}. For x, y in the domain, xAy if |x-y| is less than 2
1.The features A1 and A2 were measured for each member of two groups X and Y. The measurements are given below: Group X Feature A1 120 100 130 120 140 Feature A2 75 80 80 70 70 Group Y Feature A1 80 70 90 90 100 Feature A2 70 70 60 70 60 You are given that: Query1 has features A1 - 120, A2 - 85, and Query2 has features A1 - 90, A2 - 50. Classify Query1 and Query2 by using: Euclidean distance method 2.Apply the Apriori algorithm to the following transactional data. The data has been obtained from a popular supermarket chain in Nairobi during the school's opening week. Assume minimum support of minimum support of 25%, and minimum confidence 55%, and derive a rule or rules
Question 1 Which of the following correctly defines what a 'recurrence relation' is? O T(n)=T(n-1)+2n, T(0)=1 O T(n) = 2(1+n), T(0) = 2 An equation (or inequality) that represents nth iteration of a sequence in terms of n. That includes an initial condition. An equation (or inequality) that relates the nth element of a sequence to its predecessors (recursive case). This includes an initial condition (base case).
Given: e-NFA M2 = ({A,B,C}, {0,1}, delta, A, {C}) where delta: (A,0) -> {C}, (A,1) -> {B}, (A,e) -> null, (B,0) -> {A}, (B,1) -> null, (B,e) -> {C}, (C,0) -> null, (C,1) -> {A}, (C,e) -> null. Get the equivalent DFA of the given e-NFA. The length of the string accepted by the given e-NFA M2 is ____________. Odd Even either Odd or Even
Let R be a relation on the set of all real numbers, where (x, y) E R if and only if a - y is an integer, To show that R is anti-symmetric, we must prove which of the following statement? O For any real numbers a and y, if a - For any real numbers a and y, if a # y, then a y is an integer, then y a is an integer For any real numbers a and y, if z # y, then a O For any real numbers r and O For any real numbers a and y, if a + y, then z y is an integer and y is an integer or y y is not an integer and y a is an integer r is an integer a is not an integer a is not an integer If a #y, then z y is not an integer or y To show that Ris not anti-symmetric, we must find a counterexample satisfies which of the following statement? O For some real numbers r and y, z O For some real numbers z and y, r#y and r - y is an integer and y For some real numbers r and y, r # y and a - For some real numbers z and y, r #y and z - For some real numbers r and y, x # y and a y is an integer, and y r is not an…
Use the substitution method to identify the big-Oh of the represented by the following recurrence relation. Note: c is a constant. T(n) = cn + T(n/2) + T(n/2), T(1) = c
Determine the strongest asymptotic relation between the functions f(n)= 2log and g(n)-(logn), i.e., whether f(n) = o(g(n)), f(n) = O(g(n)), f(n) = (g(n)), f(n) = w(g(n)), or f(n) = (g(n)).
The domain for the relation R is the set of all integers. For any two integers, x and y, xRy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) Symmetric Transitive Anti-symmetric Reflexive
Given the Recurrence relation for the Binomial expansion as:C(n, k) = C(n-1, k) + C(n-1, k-1) for n > k > 0C(n,0) = 1, C(n, n) = 1 for n ≥ 0Apply the Dynamic programming to determine the Binomial coefficient C (9, 6)
The set of letters S consists of 30 As, 6 Bs, 24 Cs, 15 Ds, and 15 Es. The set of letters T consists of 25 As, 20 Bs, 15 Cs, 5 Ds and 35 Es. What is the mutual index of coincidence between sets S and T? Leave your answer as a fraction in lowest terms
QUESTION 3 The domain for the relation R is the set of all integers. For any two integers, x and y, xRy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) Anti-symmetric Reflexive Symmetric Transitive
Let A = {0, 1, 2, 3} and define relations R, S, and T on A as follows: R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}, S = {(0, 0), (0, 2), (0, 3), (2, 3)}, T = {(0, 1), (2, 3)}. a. Is R reflexive? symmetric? transitive? b. Is S reflexive? symmetric? transitive? c. Is T reflexive? symmetric? transitive?