Math 3614: Study Guide 2 (9/9-9/16)

(Your group will be evaluated on this material on 9/16)

Sections 6.4-6.5

Objectives:

Learn the following terms:
- transitive closure
- reflexive closure
- symmetric closure
- path (in a digraph)
- circuit
- cycle
- connectivity relation
- equivalence relation
- equivalence class
- representative (of an equivalence class)
- partition (of a set)
Become comfortable working the following types of problems:
1. Given a relation on a set, determine the transitive, reflexive, and symmetric closures.
2. Given a directed graph of a relation, modify the graph to produce the reflexive and symmetric closures. (See for example, Section 6.4, problems 5,6,7,9).
3. Given a directed graph, determine if there is a path of length n between two vertices.
4. Use the zero-one matrix of a relation to compute the transitive closure of the relation.
5. Given a relation on a set, determine if it is an equivalence relation.
6. Determine the equivalence classes of a given equivalence relation.
Problem List:Learn to work the following problems:
1. Section 6.4: 12, 13, 14, 25, 27
2. Section 6.5: 4, 10, 11, 14, 27

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Suggested Study Plan:

(Note: this is only a suggestion, feel free to study any way you want in order to achieve the above objectives)

Individual Preparation:
1. Read Sections 6.4-6.5
2. Review the list of terms given above, and make sure you are familiar with each.
3. You may want to work a few easy exercises to reinforce your understanding.
4. Attempt the problems in the problem list (Note: do not expect to be able to do all of these on your own).
5. Compose a small set of "test" problems which you can quiz your group members with.
Group Activities:
1. Take turns quizzing your group. For example, let one person give a problem to the other members of the group, with a short time limit. At the end of the time, discuss the solution as a group. Then let someone else pose a question; etc.
2. As a group, discuss the problems from the problem list. Try to agree on a solution to each problem. If you cannot solve a problem, or if you cannot agree on a solution, come talk to me. Make sure everyone in the group understands how to work the problems.

Evaluation:

On Monday, September 16, the above objectives will be evaluated with a group project. I will give out a set of problems which you will work as a group. Each group will turn in one set of solutions.