Indicate the properties of each of the following relations. For each relation,indicate whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, and/ortransitive. You do not need to justify your answer.1. R is a relation on set Z such that (x, y) E R if and only if x + y = 0.2. R is a relation on set Z such that (x, y) ER if and only if x and y have oppositeparity.Hint: Two integers have opposite parity if one is even and the other one is odd.

here are the properties of each relation:R is reflexive, symmetric, and transitive.R is…

Answered: Indicate the properties of each of the…

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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The division operator of relational algebra, “÷”, is defined as follows. Let r(R)and s(S) be relations, and let S ⊆ R; that is, every attribute of schema S isalso in schema R. Given a tuple t, let t[S] denote the projection of tuple t onthe attributes in S. Then r ÷ s is a relation on schema R − S (that is, on theschema containing all attributes of schema R that are not in schema S). A tuplet is in r ÷ s if and only if both of two conditions hold:• t is in ΠR−S(r)• For every tuple ts in s, there is a tuple tr in r satisfying both of the following:a. tr[S] = ts[S]b. tr[R − S] = tGiven the above definition:a. Write a relational algebra expression using the division operator to findthe IDs of all students who have taken all Comp. Sci. courses. (Hint:project takes to just ID and course id, and generate the set of all Comp.Sci. course ids using a select expression, before doing the division.)b. Show how to write the above query in relational algebra, without usingdivision. (By doing so, you…
Select all binary relation properties that apply to the following relation: Equal magnitude: |x| = lyl O antisymmetric O reflexive O symmetric O transitive
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.
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…
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).
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.
Let R be a relation on A = {0, 1, 6, 8} and R = {(0,0), (8, 6), (6, 6), (8, 8), (1, 1), (1,0), (0, 1)}. Are the following statements true or false? 1. R is symmetric ? ? ? ? ? ? V V 2. R is transitive 3. R is reflexive 4. R is an equivalence relation 5. R is anti-symmetric 6. R is a partial order
Struggling on this problem, I can see that it's incorrect and am close but I'm overlooking the flaw in reasoning somewhere.
List all 3-tuples in the relation {(a,b,c)| abc = 6} where a, b and c are all positive integers.
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?
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?
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