p.650, icon at Example 4# 1. Let R be the relation on the set of words in the English language where xRy if x precedes (that is, comes before)y in the dictionary. Show that R is not a partial ordering.

Answered: Image /qna-images/answer/24092cea-53c9-47ae-add2-3a584b2d5670.jpg

Answered: p.650, icon at Example 4 # 1. Let R be…

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

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1. Consider the relation R on the set (a,b.c,d,e,f] which is defined as follows: R-{(a,a), (a,b). (a.c). (b.a). (b.c), (c,a). (c,b). (d.d), (f.f)}. Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive? Give reasons!
Let S be a set with |S| = 5. How many relations are there on S? A. 5! В. 55 C. 520 D. 525 Е. 225 A В E C.
Design a data structure for a set in which insertions, deletions, and membership queries can be processed in O(1) tim e in the worst case. You m ay assume that the set elements are integers drawn from a finite set {1, 2,...,n}.
b) Express the following relation using a set-builder notation R = {(1, 2), (2, 6), (3,9), (4, 16), (5, 20), (6, 36), ...}
2
Let a set be represented by a list of numbers. Write the following Prolog relations: - union(A,B,C) is true if the list C contains only even numbers in either lists A or B - intersection(A,B,C) is true if the list C contains only even numbers in both lists A and B.
Q # 3; (a). The relation ‘R’ is defined on the set M=(4,5,6,7) as the following;R={(5,5),(5,6),(5,7),(6,5),(6,6),(6,7)} Check is it reflexive , symmetric and transitive. (b). Let the string having length eight of an arrays is defined as ; 01001010 , 01101101Apply the definition of Tautology on it. Q # 4; (a). Let ‘T’ and ‘S‘ are two non-empty sets which are defined as; T={x ; -1 ≤x≤1}=S and modulus function f: T→S defined by; f(x)=x|x| Check it for injective and also draw its graph(b). Simplify by using Boolean algebra definition; AB+BC+B ̅C=AB+C Q # 5. Given a simple graph G as below in figure ; Check it for the following ;Find its chromatic number which must be threeFind the degree of the graph and write it in degree sequence Label its edges and also write down its in vertex form
Question 4: Assume a generic recursive relation is defined as : A[i] = p*A[i-1] + q where p and q are coefficients of the relation. Write a function that takes the first three numbers in this relation as a list, such as [A[0], A[1], A[2]] and computes p and q, and returns A[3]. For example, given [1,3,5] your function should return 7, because the numbers 1,3,5 are produced by the series: A[i] = A[i-1] + 2 where p is 1 and q is 2, and then the next number in the series becomes 7. You can assume that p and q are always integers. You can also assume that p and q are determinable in any test case. def recursionSolver(values):
AB* tree index is to be built on the Name attribute of the relation STUDENT. Assume that all student names are of length 8 bytes, disk blocks are of size 512 bytes, and index pointers are of size 4 bytes. Given this scenario, what would be the best choice of the degree (i.e. the number of pointers per node) of the Bt - tree?
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
Define two sets: a letter set A = {t. p. c) and a word set B = {proposition, math, proof, discrete). Define the relation R = A x B such that (letter, word) is in the relation if that letter occurs somewhere in the word. Choose the correct relation R. O R = {(t, proposition), (t, proof), (p. proposition), (p. proof), (c, math), (c, proof)} O R = {(t, math), (p, proposition), (p, math), (p, proof), (c, math), (c, proof)} O R = {(t, proposition), (t, math), (t, discrete), (p. proposition), (p, proof), (c, discrete)} OR = {(t, discrete), (p. proposition), (p, math), (p. proof), (c, math), (c, discrete)}
9. of 40 Let R(A, B, C, D, E) be a relation with the set of FD's: F%3 {D — С, С — D, D —— A, C — А, Е — С, Е — А, Е — В, В —C). Which of the following statements is NOT correct? Select one: O G = {D– C, C → D, D → A, E → B, B → C} is a canonical cover (minimal basis) of F. O H= {D– C, C → D, C → A, E –→ B, B → C} is a canonical cover of F. O F is a canonical cover of itself. O Both G and H are canonical covers of F.

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p.650, icon at Example 4 # 1. Let R be the relation on the set of words in the English language where xRy if x precedes (that is, comes before) y in the dictionary. Show that R is not a partial ordering.