Unit 12 Exercises

1. Let A be a set.  Show that emptyset.gif 
(909 bytes) x A = A x emptyset.gif (909 bytes) = emptyset.gif 
(909 bytes).

2. How many different elements does A x B  have if A has m elements and B has n  elements?

3. Let A = {1, 2, 3, 4} and b = {0, 3, 5}.  Find

  1. A cup.gif (142 bytes) B
  2. A cap.gif (142 bytes) B
  3. A - B
  4. B - A

4. What can you say about the sets A and B if the following are true?

    a) A cup.gif (142 bytes) B = A

    b) A - B = A

5. Let A and B be subsets of a universal set U.  Show that A subseteq.gif (874 bytes) B if and only if B_bar.gif (177 bytes) subseteq.gif (874 bytes) A_bar.gif (163 bytes).

 

Answers for these exercises