StŠr­frŠ­imynstur Ý t÷lvunarfrŠ­i

Weekly note 10

This week we will finish up with relations from chapter 7 and then start on graphs. We will go over the main concepts related to graphs, their usage, and most important types of graphs from sections 8.1 - 8.4.

Next week we will continue with graphs and then go on to trees in chapter 9.

Below are 5 excercises that you are to solve and turn in to your section teacher before noon monday November 7th. Remember to mark your solutions with the number of your section and the name of the section teacher. Also below are few extra excercises that you can use to practice on and make sure that you have understood the material. Some of them will be solved in the sections if there is time.

Homework 9

  1. Exercise 28 in section 4.4 on page 334 in the textbook.

  2. Exercise 32 in section 5.1 on page 361 in the textbook.

  3. Exercise 10 in section 7.1 on page 480 in the textbook.

  4. [Exam '04] In each case show the smallest relation on the set { a, b, c } that have the properties. Justify in each case that the relation is the smallest one that has the properties.
    1. Transitive, not reflexive, not symmetric.
    2. Reflexive, symmetric, not transitive.
    3. Antisymmetric, symmetric, irreflexive.
    4. Transitive, asymmetric, not irreflexive.

    1. Exercise 10 in section 7.5 on page 513 in the textbook.
    2. Exercise 28 in section 7.5 on page 514 in the textbook.

Hand these exercices in before noon monday November 7th.

Also take a look at the following excercices:
From section 7.1:
7, 13, 23.
From section 7.1:
3, 7, 25, 43, 49.
From section 7.3:
5, 9, 15.
From section 7.5:
13, 19, 41.
From section 7.6:
7, 17, 27.

Remember that the above exercises are for you to practice on, and that you get the most out of them by trying to solve them yourselves (not by looking at someone else solving them!). The exercises in bold are more "interesting" than the others and it is more likely that they will be covered in the sections.

hh (hja), October 31st, 2005.