MAT 2051 Discrete Mathematics

Unit 1 Discussion

DQ1 Logic and Reasoning

Logic and reasoning play important roles in computer applications, systems management, database management, and error management. In this discussion, you will examine logic and deductive reasoning, symbols and definitions, and an application involving database and error logging.

Deductive Reasoning, Part 1

Given the following true logical statement:

If inputs x1, x2, and x3 are all true, then output y is true.

Write this statement as a logical statement using the appropriate logic symbols for conjunction and implication.

Write the converse and contrapositive of this statement.

Is the converse true? Explain why or why not.

Is the contrapositive true? Explain why or why not.

Deductive Reasoning, Part 2

Assume you are a systems manager and that you know a server will log an error message if a database has a retrieval error. With that, complete the following:

Why is it important for errors to be logged?

What is a database retrieval error, and what might cause this type of error?

If you notice that there is an error logged, can you infer that a retrieval error has occurred without reading the log? Explain why or why not. (Hint: This is a question about reasoning.)

Prior to posting your response, review the Discussion Participation Scoring Guide. This is the recommendation for all discussions in this course.

Response Guidelines

Read your peers’ posts and respond to two. Do you agree with your peer’s assessment of the problem? Explain.

DQ2 Practice Problem Set Review

The problem sets are assigned to help you practice solving problems and prepare for the corresponding quiz and the final exam. As mentioned in the studies, the problem sets are not graded or collected.

Each unit you will have an opportunity to discuss the problem sets with your fellow learners. Use this discussion to ask questions, make comments, ask for help, and assist your peers with the problem sets. Teamwork is encouraged.

Four posts are required in this discussion: two initial and two response. Additional posts are optional and recommended, but not required for your grade:

For the first post, select a problem from this unit’s problem set, write it out fully, solve it fully, and post it.

The second post can be a problem you cannot solve or another fully solved problem from the problem set. If there is a problem in the assigned problem set that you are confused about, write it out fully and show any work you have started. Note that you are stuck and ask for help. If you are able to solve every problem in the set without difficulty, post at least one other fully solved problem from the set as your second post.

The third and fourth posts are response posts. Response guidelines are provided below and in every discussion.

Take advantage of this discussion area to work together as a class on the problem set. Post as many problems as you can and review as many of your peers’ posts as you can. Ask questions. Offer answers. If you are stuck on a problem, post your question. Working as a team will help each person gain a better understanding of the problem set and the concepts covered in this unit.

Response Guidelines

The third and fourth posts, the response posts, are your chance to help your peers. Explore the posts made by your peers and find people who are stuck. Help at least two peers through the problems they are stuck on. If you are unable to locate a peer who is stuck, you may instead choose a peer post, write out your solution to the same problem, and compare solutions and methods. The goal of this area is for the entire class to work together as a group on the entire problem set. You are also expected to complete and understand the problem set on your own in preparation for the quizzes and final exam.