Homework 3 (assigned July 6, due July 12)

1. Exercises 26, 27, 42, and 81 on page 86.   (1 point each)

2. Find the sets A and B if A - B = {1, 5, 7, 8}, B - A = {2, 10}, and A ∩ B = {3, 6, 9}.   (2 points)

3. Can you conclude that A = B if A, B, and C are sets such that
   • A ∪ C = B ∪ C

   • A ∩ C = B ∩ C

   Justify your answers.   (2 points each)

4. Let A and B be sets. Show that A ⊆ B if and only if A ∩ B = A.   (3 points)

5. Let A, B, and C be sets. Show that (A - B) - C is not necessarily equal to A - (B - C).   (3 points)

6. Exercise 94 on page 87.   (2 points for each part)

7. Exercises 8 and 17 on pages 60 and 61.   (3 points each)

8. Exercises 36, 46, and 54 on page 124.   (3 points each)

9. Let R be the relation {(1,2), (1,3), (2,3), (2,4), (3,1)} and S be the relation {(2,1), (3,1), (3,2), (4,2)}. Find S o R.   (2 points)

10. List the 16 different relations on the set {0,1}, i.e., {0,1} x {0,1}. How many of these relations contain the pair (0,1)?   (3 points)

11. Exercises 12 and 13 on page 136.   (2 points each)

12. Exercise 31, parts (a) and (c) (2 points for each part), and exercises 44 and 45 on page 130 (3 points each). Show that R is transitive if and only if R o R ⊆ R.   (4 points)

Gerry Brady
Wednesday July 6 23:25:01 CDT 2005