Please answer it perfectly Exercise 5 Here is a directed graph that represents a relationover the set of vertices V = {1,2,...,11}:1E = {(a, b) | there is a directed edge from vertex a to vertex b}526374891011(a) Write out the ordered pairs in the relation E represented by the graph.(b) Define the relation R(a, b) to mean (a = b) V E(a, b). Draw the graph with the minimalnumber of vertices and edges, describing the relation R over the same vertices V, for which thefollowing logical expression is true:Va € V. Vb € V. R(a, b)(c) Define the relation S(a, b) to mean R(a, b)VE(b, a). Draw the directed graph with the verticesV and minimal number of edges, describing the relation S over the same vertices V, for which thefollowing logical expression is true:Va € V.Vb € V. S(a, b)(d) Draw the graph with the vertices V and minimal number of edges, describing a relation Tfor which the following logical expression is true:Va V. Vb € V. [S(a, b) → T(a, b)] AVce V. (T(a, b) A T(b, c) → T(a, c))Describe the relation T(a, b) simply in under 10 words.

A directed graph which represents that it is graph with a set of objects (called vertices or nodes)…

Exercise 5 Here is a directed graph that represents a relation E = {(a, b) | there is a directed edge from vertex a to vertex b} over the set of vertices V = {1,2,..., 11}: 5 2 6 3 7 4 8 9 10 11 (a) Write out the ordered pairs in the relation E represented by the graph.

Exercise 5 Here is a directed graph that represents a relation E = {(a, b) | there is a directed edge from vertex a to vertex b} over the set of vertices V = {1,2,..., 11}: 5 2 6 3 7 4 8 9 10 11 (a) Write out the ordered pairs in the relation E represented by the graph.

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 A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using directed graph
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Let A ={1, 2, 3, ... , 10}, B = {2, 3, 6, 8}, and C = {3, 5, 4, 8, 2} Write the Venn diagram representation of the following sets. How many elements are there in A U B U C.
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Question 1: In graph theory, a graph X is a "complement" of a graph F if which of the following is true? Select one: a. If X is isomorph to F, then X is a complement of F. b. If X has half of the vertices of F (or if F has half of the vertices of X) then X is a complement of F. c. If X has the same vertex set as F, and as its edges ONLY all possible edges NOT contained in F, then X is a complement of F. d. If X is NOT isomorph to F, then X is a complement of F. Question 2: Which statement is NOT true about Merge Sort Algorithm: Select one: a. Merge Sort time complexity for worst case scenarios is: O(n log n) b. Merge Sort is a quadratic sorting algorithm c. Merge Sort key disadvantage is space overhead as compared to Bubble Sort, Selection Sort and Insertion Sort. d. Merge Sort adopts recursive approach