For the following relations on the set of college students, determine if it satisfies each of the following conditions: Symmetric A ~ B⇒ A is strictly taller than B A B A, B took 3 class(es) together N A~ B⇒ A, B have the same major Please enter Y or N in each of the boxes. Reflexive Transitive Equivalence Relation

For the following relations on the set of college students, determine if it satisfies each of the following conditions: Symmetric A ~ B⇒ A is strictly taller than B A B A, B took 3 class(es) together N A~ B⇒ A, B have the same major Please enter Y or N in each of the boxes. Reflexive Transitive Equivalence Relation

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 USES relation naturally forms a graph. As mentioned in the lecture, the USES relation graph should be a Directed Acyclic Graph (DAG). (1) A graph could be represented with two different data structures, i.e., adjacency list and adjacency matrix. Represent the USES relation graph in Figure 3-1 with adjacency list and adjacency matrix. 3 2 4 5 6. Figure 3-1: USES relation graph of the modules in a system (2) Suppose the input of a USES relation graph is represented with adjacency list, develop a function in pseudocode to check whether the USES relation graph is an acyclic graph, using Stepwise Refinement technique taught in lectures. You should provide with at least 2 refinements. Assuming there are V vertices and E edges, please state the time complexity of your algorithm.
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?
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1. Let A = {3, 4, 5} and B = {4, 5, 6} and let S be the "divides" relation. That is, for all (x, y) ≤ A × B, xSy ↔ x|y. State explicitly whic ordered pairs are in S and S-1
Determine whether the given relation is reflexive, symmetric, anti-symmetric and transitive (x, y)∈R if and only if y=x is less than and equal to x^2
choose all the correct ones:
Let R be a relation on the set of all real numbers, where (x, y) E R if and only if a - y is an integer, To show that R is anti-symmetric, we must prove which of the following statement? O For any real numbers a and y, if a - For any real numbers a and y, if a # y, then a y is an integer, then y a is an integer For any real numbers a and y, if z # y, then a O For any real numbers r and O For any real numbers a and y, if a + y, then z y is an integer and y is an integer or y y is not an integer and y a is an integer r is an integer a is not an integer a is not an integer If a #y, then z y is not an integer or y To show that Ris not anti-symmetric, we must find a counterexample satisfies which of the following statement? O For some real numbers r and y, z O For some real numbers z and y, r#y and r - y is an integer and y For some real numbers r and y, r # y and a - For some real numbers z and y, r #y and z - For some real numbers r and y, x # y and a y is an integer, and y r is not an…
For each of the following relations, determine whether the relation is: • Transitive. • A partial order. • A strict order. • An equivalence relation. Reflexive. Anti-reflexive. Symmetric. • Anti-symmetric. Justify all your answers. a. Ris a relation on the set of all people such that (a, b) e R if and only if a and b have a common grandparent. b. Ris a relation on Z such that (x, y) E R if and only if |x – y| < 2. c. Ris a relation on Z* such that (x, y) E R if and only if x is divisible by y. Hint: An integer x is divisible by an integer y with y # 0 if and only if there exists an integer k such that x = yk. d. Ris a relation on Z* such that (x, y) E R if and only if there is a positive integer n such that x" = y. e. Ris a relation on Z x Z such that ((a, b), (c, d)) E R if and only if a < c and b < d.
QUESTION 3 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.) Anti-symmetric Reflexive Symmetric Transitive
discrete answer please as soon as possible