Answer these questions for the poset ({2,4, 6, 9, 12,18, 27, 36, 48, 60,72} ,|), where "I" represents the "divides" relation. (Hint: create a Hasse diagram.) Find the maximal elements. Find the minimal elements. Is there a greatest element? Is there a least element? Find all upper bounds of {2, 9}. Find the least upper bound of{2, 9}, if it exists. Find all lower bounds of {60, 72}. Find the greatest lower bound of {60, 72}, if it exists.

Answer these questions for the poset ({2,4, 6, 9, 12,18, 27, 36, 48, 60,72} ,|), where "I" represents the "divides" relation. (Hint: create a Hasse diagram.) Find the maximal elements. Find the minimal elements. Is there a greatest element? Is there a least element? Find all upper bounds of {2, 9}. Find the least upper bound of{2, 9}, if it exists. Find all lower bounds of {60, 72}. Find the greatest lower bound of {60, 72}, if it exists.

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

Suppose R is a relation with attributes A1, A2, ..., An. As a function of n, tell how many superkeys R has, if The only keys are A1 and A2?
Give some instances of relationships that may have more than one candidate key to consider.
It is possible to construct a connection such as sec course from a group of relationships that are many to one. Does the relation's many-to-one cardinality restriction get enforced by the main and foreign key constraints? Why do you think that is?
Consider the issue of interesting orders in optimization. Suppose you are given a query that computes the natural join of a set of relations S. Given a subset S1 of S, what are the interesting orders of S1?
For each question in this section, you are required to decompose the given relation into BCNF form and state any new relations created in the process with their functional dependencies and identify any functional dependencies which are lost during the decomposition. You must show your working using the tree method presented in tutorials. Consider the functional dependencies in the order presented in the question. Question 1 R [A, B, C, D, E, F, G, H, I, J] {A} -> {B, C} {B} -> {D, E, F} {C} -> {G, H, I} {H, I} -> {F, J} Question 2 R [A, B, C, D, E, F, G, H] {A, B, C} -> {D, E, F, G} {G, H} -> {A, B, C} {C} -> {H}
Suppose RR is a relation with attributes A1,A2,…,AnA1,A2,…,An. How many superkeys will RR have if a) The only candidate key is A1A1. b) The only candidate keys are A1A2A1A2 and A1A3A1A3.
Suppose we have three relations r(A, B), s(B, C), and t(B, D), with all attributesdeclared as not null. Are there instances of r, s, and t such that the result ofr natural left outer join (s natural left outer join t) has a null value for C but a non-null value for D? Explain why or why not.
Given a set A = {1, 2, 3, 4}, which of the following relations is a partial order relation andwhich is not? Justify your answer(a) { (1, 2), (2, 3), (1, 3), (4, 3) }(b) { (1, 2), (2, 3), (1, 3), (3, 4), (1, 1), (2, 2), (3, 3), (4, 4) }(c) { (1, 2), (2, 3), (1, 3), (4, 3), (1, 1), (2, 2), (3, 3), (4, 4) }
Chaos does not produce order and structure. Why don't you provide some instances to back up your claim?
Consider the join R ▷◁ S where the join predicate is R.a = S.b, given the following metadata about R and S: Relation R contains 2,000 tuples and has 10 tuples per block Relation S contains 10,000 tuples and has 10 tuples per block Attribute a of relation R is the primary key for R, and every tuple in R matches 5 tuples in S There exists a primary index on S.b with height 3 There exists a secondary index on R.a with height 2 The buffer can hold 5 blocks For this problem, we use a simplified cost model where cost = number of I/O in terms of pages (i.e., the number of pages read/written). If R ▷◁R.a=S.b S is evaluated with a block nested loop join, which relation should be the outer relation? Justify your answer. What is the cost of the join in number of I/O’s?
Consider the join R ▷◁ S where the join predicate is R.a = S.b, given the following metadata about R and S: Relation R contains 2,000 tuples and has 10 tuples per block Relation S contains 10,000 tuples and has 10 tuples per block Attribute a of relation R is the primary key for R, and every tuple in R matches 5 tuples in S There exists a primary index on S.b with height 3 There exists a secondary index on R.a with height 2 The buffer can hold 5 blocks What is the cost of a plan that evaluates this query using sort-merge join. Show the details of your cost analysis. Please show detailed explaination.
Every weak entity set can be converted to a strong entity set by simply adding theappropriate attributes. Why, then, do we have weak entity sets?