For each of the following partial orders, draw a Hasse diagram, find the maximal and minimal elements, and determine whether the partial order is a total order. a. Ris a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) € R if and only if x > y. b. R is a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) e R if and only if x is a multiple of y. Hint: An integer x is a multiple of an integer y if and only if x is divisible by y.

For each of the following partial orders, draw a Hasse diagram, find the maximal and minimal elements, and determine whether the partial order is a total order. a. Ris a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) € R if and only if x > y. b. R is a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) e R if and only if x is a multiple of y. Hint: An integer x is a multiple of an integer y if and only if x is divisible by y.

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

How to code in Python or Java below Algorithm # 10 General Algorithm for Testing Loosless Join DecompositionInput: A universal relation R, a decomposition D={R1,R2,...Rm}of R , and a set F of functional dependencies.1. Create an initial matrix S with one row for each relation Riin D, and one column for each attribute Aj in R.2. Set S(i,j)= bij for all matrix entries.( Note that each bij isa distinct symbol associated with indices (i,j) ).3. For each row i representing relation schema RiFor each column j representing attribute AjIF the relation Ri includes attribute Aj then set S(i,j)= aj.( Note that aj is a distinct symbol associated with index j)4. Repeat the following loop until a complete loop execution results in no changes to SFor each functional dependency X→Y in FFor all rows in S that have the same symbols in the columns corresponding toattributes in X.Make the symbols in each column that correspond to anattribute in Y be the same in all these rows as follows:▪ If any of the…
How to code in Python or Java below Algorithm # 10 General Algorithm for Testing Loosless Join DecompositionInput: A universal relation R, a decomposition D={R1,R2,...Rm}of R , and a set F of functional dependencies.1. Create an initial matrix S with one row for each relation Riin D, and one column for each attribute Aj in R.2. Set S(i,j)= bij for all matrix entries.( Note that each bij isa distinct symbol associated with indices (i,j) ).3. For each row i representing relation schema RiFor each column j representing attribute AjIF the relation Ri includes attribute Aj then set S(i,j)= aj.( Note that aj is a distinct symbol associated with index j)4. Repeat the following loop until a complete loop execution results in no changes to SFor each functional dependency X→Y in FFor all rows in S that have the same symbols in the columns corresponding toattributes in X.Make the symbols in each column that correspond to anattribute in Y be the same in all these rows as follows:▪ If any of the…
1. A known relationship mode of R (U, F), U= (A, B, C, E, F, G, H, I, J, G); F={AB->E,ABE->FG, B->FI, C->J, CJ->I, G->H}; find the minimum cover of F, then use theNormal Form decomposition algorithm to decompose this mode to 3NF, and check if thedecomposition has the nonadditive join property.
Convert the following relation to 2NF, and then to 3NF. Show both conversions. (h, n, c, a, f, k, p, r, g, i, m, b, o, d, j, l, s, e) Functional Dependencies: p → j m, b → l h → g n → p n → o c → i n → j p → o h → d s → e a → r
¡.Determine whether the below schedule is serializable or not with suitable justifications. Draw the precedence graph as well. ii. Consider the following relations employees (empld, emp_name, Cid, dept_name, designation, salary); company (Cid, company name, city); managers (managerld, mname, Cid, no-of-indoor-projects, outdoor-project-area) Write relational algebraic expression for the following queries: a. List the salary of employees from 'Accounts department order by employee name in ascending order. b. Display the manger names along with their company name whose outdoor-project area is 'Urban'.
1. A known relationship mode of R (U, F), U= (c, t, h, r, s, g, q); F={c->tq, cs->g, ht->r,hr->c, hs->r}; find the minimum cover of F, then use the Normal Form decompositionalgorithm to standardize this mode to 3NF, and check if the decomposition has thenonadditive join property.
1.A known relationship mode of R (U, F), U= (A, B, C, D, E, G); F={AB->C, D->EG,C->A, BE->C, BC->D, CG->BD, ACD->B, CE->AG}; find the minimum cover of F,then use the Normal Form decomposition algorithm to decompose this mode to 3NF, andcheck if the decomposition has the nonadditive join property.
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}
Consider the relation R(O,P,X,Y,E, S); FDs={ O=P, XY=O, OE=S, EY=X, PY=X} What is the dependency preservation property for a decomposition? Why is it important? Decompose the relation into BCNF relation. What is the lossless (or nonadditive) join property of a decomposition? Why is it important? Determine whether each of the decompositions has the lossless join property with respect to F and conclude for the whole decomposition Determine whether each of the decompositions has the dependency preserving property with respect to FD and conclude for the whole decomposition
A relation, R, on non-empty set A is defined as a subset of A × A: R ⊆ A × A For example, let A = {1, 2, 3} then Cartesian product A × A = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}. A binary relation R ⊆ A × A Briefly explain the meaning of the relation, providing an example (and diagram): (i)) Discuss the real-life applications of binary relations
Show that the following decomposition of the schema R of Exercise 7.1 is not alossless decomposition:(A, B, C)(C, D, E).Hint: Give an example of a relation r(R) such that ΠA, B, C (r) ⋈ ΠC, D, E (r) ≠ r
J 1 Let R(A, B, C, D, E, F) be a relation schema, and let S = {A → B, BC → D, E → C, D →A, B → D} be a set of functional dependencies. Use the Nonadditive Join Test for Binary Decomposition to determine if the following decomposition is lossless.