For each of the following partial orders, draw a Hasse diagram, find the maximal and minimal elements, and determine whether the partial order is a total order. a. Ris a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) € R if and only if x > y. b. R is a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) e R if and only if x is a multiple of y. Hint: An integer x is a multiple of an integer y if and only if x is divisible by y.

For each of the following partial orders, draw a Hasse diagram, find the maximal and minimal elements, and determine whether the partial order is a total order. a. Ris a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) € R if and only if x > y. b. R is a partial order on set {2, 4, 5, 7, 10, 25, 40} such that (x, y) e R if and only if x is a multiple of y. Hint: An integer x is a multiple of an integer y if and only if x is divisible by y.

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.
B
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Discrete Math
please help for parts a and b. i want the precedence graph actually displayed
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