Define relations R₁,..., R6 on {1, 2, 3, 4} byR₁ = {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3,4)},R2 = {(1, 1), (1,2), (2, 1), (2, 2), (3, 3), (4, 4)},R3 = {(2,4), (4, 2)},R4 = {(1, 2), (2, 3), (3, 4)},R5 = {(1, 1), (2, 2), (3, 3), (4, 4)},R6 = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)},Which of the following statements are correct?Check ALL correct answers below.A. R2 is not transitiveB. R5 is not reflexiveOC. R4 is antisymmetricD. R₁ is reflexiveE. R6 is symmetricF. R4 is transitiveG. R5 is transitiveOH. R₁ is not symmetricOI. R3 is symmetricJ. R3 is transitiveK. R₂ is reflexiveL. R3 is reflexiveM. R4 is symmetric

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Answered: Define relations R₁,..., R6 on {1, 2,…

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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Let R1 and R2 be the relations on {1, 2, 3, 4} given by 6. R, = {(1,1), (1,2), (3,4), (4,2)} R, = {(1,1), (2,1), (3,1), (4,4), (2,2)}. (i) List the elements of R, R, and R, UR,. (ii) Represent digraphs for R1 and R2.
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For A = {1,2,3,4,5}, the following are equivalence relations on A: R1 = {(1,1), (1,2), (2,1), (2,2,), (3,3), (3,4), (4,3), (4,4), (5,5) R2 = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,4), (4,5), (5,4), (5,5) a. Determine the (0,1) relation matrix for each of the equivalence relations above. b. If A = {1,2,3,4,5} and R is the equivalence relation on A that induces the partition A = {1,2} U {3,4} U (5}, what is R?
Given: Relation R = {(a,a), (a.b), (b,a). (b,b). (c,c)} and Set S = {a, b, c} Complete Relation R to be Transitive with Set S
Implement in Python / Java Algorithm: Testing for lossless (nonadditive) join property. Input: A universal relation R, a decomposition D = { R1, R2, R3, ….. Rm } of R, and a set F of functional dependencies. 1. Create an initial matrix S with one row i for each relation in Ri in D, and one column j for each attribute Aj in R. 2. Set S(i, j) := bij for all matrix entries. (* each bij is a distinct symbol associated with indices (i, j) * ) {for each column j representing attribute Aj {if (relation Ri includes attribute Aj ) then set S(I, j):=aj;};}; (* each aj is a distinct symbol associated with index (j) *) 3. For each row i representing relation schema Ri {for each functional dependency X → Y in F {for all rows in S which have the same symbols in the columns corresponding to attributes in X {make the symbols in each column that correspond to an attribute in Y be…
Let R be the relation on the set {a,b,c,d} containing the ordered pairs (a,a), (a,c), (b,b), (b,c), (b,d), (c,b), (c,c), (d,a) and (d,d). Find R².
DISCRETE MATHEMATICS
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.
Can renaming be pushed through join and selection—that is, which of the following algebraic laws hold? ρN (RS) = ρN (R)ρN (S) , ρN (σC (R)) = σC (ρN (R)) In each case, support your answer by an example (i.e., give relations and parameters so that the expressions on the two sides of = are equal or non-equal). If your answer is no, additionally impose restrictions on the parameters (i.e., N and C) so that the law holds.
a
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
Write pseudocode for an iterator that implements indexed nested-loop join, where the outer relation is pipelined. Your pseudocode must define the standard iterator functions open(), next(), and close(). Show what state information the iterator must maintain between calls.

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