Purchase Solution

Discrete Math and Divides in Relation

Not what you're looking for?

Ask Custom Question


16. Consider the “divides” relation on the following set A. Draw the Hasse diagram for the relation. (See Overview for drawing tips.)
b. A = {2, 3, 4, 6, 8, 9, 12, 18}

23. Find all greatest, least, maximal, and minimal elements for the relation in #16b.

42. Use the algorithm given in the text to find a topological sorting for the relation of exercise #16b that is different from the “less than or equal to” relation  . (You only need to write down your sorting; it is not required to show the steps.)

46. A set S of jobs can be ordered by writing x  y to mean that either x = y or x must be done before y, for all x and y is S. Please see Hasse diagram for this relation on page 601 for a particular set S of jobs:
a. If one person is to perform all the jobs, one after another, find an order in which the jobs can be done.

b. Suppose enough people are available to perform any number of jobs simultaneously.
(i) If each job requires one day to perform, what is the least number of days needed to perform all ten jobs?

(ii) What is the maximum number of jobs that can be performed at the same time?

47. Suppose the tasks described in Example 10.5.12 require the following performance times:
Task Time Needed to
Perform Task
1 9 hours
2 7 hours
3 4 hours
4 5 hours
5 7 hours
6 3 hours
7 2 hours
8 4 hours
9 6 hours
a. What is the minimum time required to assemble a car? (Do NOT bother to turn in the Hasse/PERT diagram. Just indicate what numbers you’ve added to get the minimum time, and the order in which you added them.)

b. Find a critical path for the assembly process.

48. Section 10.2, #22. Determine whether or not the given binary relation is reflexive, symmetric, transitive, or none of these. Justify your answers.

Let SIGMA = {0, 1} and A = SIGMA*. A binary relation G is defined on SIGMA* as follows:
For all s, t in SIGMA*, s G t iff the number of 0's in s is greater than the number of 0's in t.

49. Section 10.2, #17. Determine whether or not the given binary relation is reflexive, symmetric, transitive, or none of these. Justify your answers.

O is the binary relation defined on Z as follows:
For all m, n in Z, m O n iff m - n is odd.

Purchase this Solution

Solution Preview

<br>(16) The Hasse Diagram is as follows.There are four lines added which are from 2 to 6, 3 to 9, 4 to 12, and 6 to 18 respectively.
<br> 2------->4-------->8
<br> 3------->6-------->12
<br> 9-------->18
<br>(23) Solution.
<br> The greatest element is 18 since there is no element which bigger than 18 and can be divided by 18. So 2 should be the least one.
<br>The maximal elements are 8, ...

Solution provided by:
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution

Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.