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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4. Write the relation matrix for the relation R on the set (a,b.c.d.e.f) which is defined as follows: R={a,a), (a,b), (a,c), (b,a). (b,c). (c,a), (c,b), (d,d), (f.f).
Consider the collection of functions qux(), plg), foo(), and dwd(), each of each is associated with an unspecified operation that has a worst-case time complexity specified below. The function call "qux0" is an operation with a worst-case time complexity of e(n) The function call "plg0" is an operation with a worst-case time complexity of e(n2) The function call "foo0" is an operation with a worst-case time complexity of e(n) The function call "wcr0" is an operation with a worst-case time complexity of e(n) The function call "dwd0" is an operation with a worst-case time complexity of e(n²) Which of the following time complexity assertions would best describe the code fragment that is also presented below? n.b., If more than one of the available options are correct, then you must select only the smallest. a = n while (a > 1): c = n while (c > 1): u = n while (u > 1): qux () u = 1 1 = n while (1 > 1): plg () 1 = 1 - 1 foo () c = c / 2 p = n^2 while (p > 1): wcr () p = p - 1 dwd () а а -…
Let R be a relation on A = {0, 2, 7, 8} and R = {(7, 2), (8, 8), (8, 0), (2, 7), (2, 2), (7,0)}. Are the following statements true or false? 1. R is an equivalence relation ? ? ? ? ? ? V 2. R is reflexive ✓ 3. R is transitive 4. R is anti-symmetric 5. R is a partial order 6. R is symmetric
1. Consider the relation R on the set (a,b.c,d,e,f] which is defined as follows: R-{(a,a), (a,b). (a.c). (b.a). (b.c), (c,a). (c,b). (d.d), (f.f)}. Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive? Give reasons!
2. Let A = {0,1}. Determine all relations on A.
let R be a relation defined on the set z by aRb if a < b. What property/properties are violated? A. Symmetric & transitive B. Reflexive & Symmetric C. Reflexive & Transitive D. All three properties
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
Question 3 • Let A be the set A={a,b,c,d} and R is a relation on set A, where R = { (a,a), (a,b) ,(b,a),(b,b), (c,d),(c,c) ,(d,d)} Determine if R is a reflexive and symmetric relation on A.
For each of the following pairs of expressions, give instances of relations thatshow the expressions are not equivalent. ΠA(r − s) and ΠA(r) − ΠA(s).
The following digraph represents a relation R. a C b d List the ordered pairs in the relation. R = { }.
Let X= {4,5,6}.If we define a relation R on X by (x,y)=R if x
The domain for the relation R is the set of all integers. For any two integers, x and y, xRy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) Symmetric Transitive Anti-symmetric Reflexive

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