Math 3614: Study Guide for Week 1 (8/26-9/9)

Sections 6.1-6.3

Objectives:

1. Learn the following terms:
   • binary relation from A to B
   • relation on a set A
   • properties of relations:
     1. reflexive
     2. symmetric
     3. antisymmetric
     4. transitive
   • inverse relation (R^(-1))
   • n-ary relation
   • domain
   • degree
   • relational data model
   • primary key
   • composite key
   • projection
   • join
   • zero-one matrix
   • digraph
   • vertex
   • node
   • edge
   • initial vertex
   • terminal vertex
   • loop
2. Become comfortable working the following types of problems:
   1. Represent a given relation graphically (see pg 357, figure 2).
   2. Given a relation on a set, determine which properties hold (see section 6.1, problems 3,4,5).
   3. Given two relations, state the composition of the two.
   4. Given a relation R on a set, determine the relation R^n.
   5. Given a table description of an n-ary relation, perform a projection operation to form a new table with fewer fields.
   6. Given two tables, perform a join operation to create a new table.
   7. Given a description of a relation, represent the relation using a zero-one matrix.
   8. Describe simple ways to tell if a relation is symmetric, reflexive, or anti-symmetric, by looking at the matrix representing the relation.
   9. Given a description of a relation, represent the relation using a digraph.
   10. Given a digraph, determine whether the associated relation is reflexive, symmetric, antisymmetric, and/or transitive.
3. Problem List:Learn to work the following problems:
   1. Section 6.1: 12, 13, 27, 28
   2. Section 6.2: 9, 11
   3. Section 6.3: 7,8,9,13,14,15

Suggested Study Plan:

• Individual Preparation:
  1. Read Sections 6.1-6.3
  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: (There will be 30 minutes given in class on 8/28 and 9/4 for group activities, however, you may want to arrange additional time to meet with your group).
  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: