StŠr­frŠ­imynstur Ý t÷lvunarfrŠ­i

Weekly note 4

This week we will finish up with functions (1.8) and then cover algorithms and their analysis in chapter 2 (2.1 - 2.3).

Next week we will continue with the second half of chapter 2 on integers and number theory.

Below are 5 excercises that you are to solve and turn in to your section teacher before noon monday september 26th. 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 4

  1. [Exam 2004] Prove the following statements using the rules in section 1.2 Ý the textbook (page 24). In each step show which rule you are using. Do not use truth tables.
    1. The proposition ((Øp Ú q) Ù (p Ú r)) ® (q Ú r) is a tautology.
    2. The proposition (p Ù Øq Ù r) Ú (p Ù Øq Ù Ør) is logically equivalent to Ø(p ® q).

  2. Exercise 12 in section 1.6 on page 85 in the textbook.

  3. Exercise 6 a), h) in section 1.7 on page 95 in the textbook.

  4. Exercise 10 in section 1.8 on page 109 in the textbook.

  5. Exercise 36 in section 1.8 on page 110 in the textbook.

Hand these exercices in before noon monday september 26th.

Also take a look at the following excercices:
From section 1.6:
3, 7, 13, 17, 25.
From section 1.7:
7, 15, 21, 27.
From section 1.8:
3, 13, 15, 19, 31, 35, 37 45.

Please note that the above exercises are for you to practice on, and that they are only useful to you if you try 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.

For those who want to go deeper into set theory, you might want to look at Exercises 51-53 on pages 96-97. It looks at fuzzy sets. On the homepage of the textbook there is a pointer to more material on this subject. Also there is a rather good collection of pointers on fuzzy sets and fuzzy logic.

hh (hja), September 20st, 2005.