Homework 2 - CS330

**Due Date: 9/17/97**

I. (10+10+10+10 points)

- Determine the set A = { x | x = (6n + 7)/(3n +1) } where x and n are integer numbers
- Describe the sets: P(P({2})) and P(P(P({2})))
- What of the following propositions are true or false:

- {a, b, c} = { b, a, c}
- 3 Î {3 }
- 3 Ì {3}
- {3} = {{3}}
- Æ = {1}
- Æ Î {1}
- Æ Ì {1}
- A x B = B x A (prove the relation)

- Consider that a is a natural number and the following notation:

D(a) = { x | x divides a } where x is a natural number

- Prove that D(a) has at least 2 elements
- For what natural numbers a, D(a) has exactly two elements
- For what natural numbers a, D(a) has exactly four elements
- Determine the sets: D(8), D(160), D(120)

II. (10+10 points)

- Exercise 21 pp. 83 (textbook)
- Given the alphabet A = {0,1}, determine the language: L = { x Î A* | (x is a palindrome) Ù (|x| £ 6)}

III. (10+5+5+5 points)

- Exercise 59 pp. 101
- R = { (x, y) | x = y – 1 , x, y Î {1,2,3,4,5} } , determine the set of all elements of the relation R
- Exercise 44, pp.101
- Exercise 57, pp. 101

Total 85 points (100%)