p.629, icon at Example 2# 1. Let R be the relation on {1,2, 3, 4} such thatR = {(1, 1), (1, 4), (2, 3), (3, 1), (3, 3), (4, 4)}.Find:(a) the reflexive closure of R.(b) the symmetric closure of R.(c) the transitive closure of R.

Answered: p.629, icon at Example 2 # 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

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Can you help me with part 1 please? Thanks
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Part 1 Let R be an equivalence relation on A = {0, 2, 3, 5} and R= {(5,5), (0, 2), (3, 3), (2, 0), (2, 2), (0, 0)}. There are defined by R. Part 2 unique equivalence classes
21. of 40 A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if every decomposed relation is in BCNF. Let R(A,B,C,D,E,F,G) be a relation with the functional dependencies: C→ E, EG→ D, DG-→A, and A→ BF. If we decompose R into relations R1(C, D, G), R2(A, D, G), R3(A, B, F), and R4(C, E), which of the following statements is TRUE? Select one: O The decomposition is in BCNF but Not in 3NF. The decomposition is in 3NF and in BCNF. The decomposition is in 3NF but Not in BCNF. O The decomposition is Not in 3NF and Not in BCNF.
1) What are the canidate keys 2) waht is the canonical cover of this relation
Consider the relation R on Z? given by: R = {((a, b), (c, d)) : a +d = c+b} Prove that R is an equivalence relation, and determine 3 elements of [(1,3)], the equivalence class of (1, 3).
5 of 40 A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if every decomposed relation is in BCNF. Let R(A,B,C,D,E,F,G) be a relation with the FDs: F = {CD → G, DG → C, AD→ G, G –→A, AB → F}. Consider the decomposition of R into R1(C, D, G), R2(A, D, G), R3(A, B, F) and R4(C, E). Which of the following statements is TRUE about this decomposition? Select one: O Ris in BCNF but Not in 3NF. Ris in 3NF but Not in BCNF. R is Not in 3NF and Not in BCNF. O R is in 3NF and in BCNF.
a) Define a relation R on R (the set of all real numbers) as follows: For all x, y E R, xRy → x < y. Is R reflexive, symmetric and transitive?
B
p.609, icon at Example 2 # 2. Let A be the set of all points in the plane with the origin removed. That is, Define a relation on A by the rule: A = {(x, y)|x, y = R} - {(0,0)}. (a, b)R(c, d) ↔ (a, b) and (c, d) lie on the same line through the origin. (a) Prove that R is an equivalence relation. (b) Describe the equivalence classes arising from the equivalence relation R in part (a). (c) If A is replaced by the entire plane, is R an equivalence relation?
1. Let A = {3, 4, 5} and B = {4, 5, 6} and let S be the "divides" relation. That is, for all (x, y) ≤ A × B, xSy ↔ x|y. State explicitly whic ordered pairs are in S and S-1
Question 17 Please provide the answer wisely.

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p.629, icon at Example 2 # 1. Let R be the relation on {1,2, 3, 4} such that R = {(1, 1), (1, 4), (2, 3), (3, 1), (3, 3), (4, 4)}. Find: (a) the reflexive closure of R. (b) the symmetric closure of R. (c) the transitive closure of R.