Homework 2 - CS330

 Due Date: 9/17/97

 

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

  1. Determine the set A = { x | x = (6n + 7)/(3n +1) } where x and n are integer numbers
  2. Describe the sets: P(P({2})) and P(P(P({2})))
  3. What of the following propositions are true or false:
    1. {a, b, c} = { b, a, c}
    2. 3 Î {3 }
    3. 3 Ì {3}
    4. {3} = {{3}}
      5.
    5. Æ = {1}
    6. Æ Î {1}
    7. Æ Ì {1}
    8. A x B = B x A (prove the relation)

 

  1. Consider that a is a natural number and the following notation:

D(a) = { x | x divides a } where x is a natural number
    1. Prove that D(a) has at least 2 elements
    2. For what natural numbers a, D(a) has exactly two elements
    3. For what natural numbers a, D(a) has exactly four elements
    4. Determine the sets: D(8), D(160), D(120)

 

II. (10+10 points)

  1. Exercise 21 pp. 83 (textbook)
  2. 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)

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

 

Total 85 points (100%)