Practice Homework 4 -- Sets I

1. Let A = {a, { }}. Which of the following are true?

   ____	a is an element of A
   ____	a is a subset of A
   ____	{a} is an element of A
   ____	{a} is a subset of A
   ____	{ } is an element of A
   ____	{ } is a subset of A
   ____	{{ }} is a subset of A
   ____	The cardinality of A is 1.
   ____	The cardinality of A is 2.
   

2. Find two finite sets A and B such that A is an element of B and A is also a subset of B.

3. Find the power set of {a, {a}}.

4. List five elements of the set {x | x=3k+5 and k is a natural number}.

5. Draw 2-set Venn diagrams to illustrate each of the following:
   • A-B
   • (A union B)-(B-A)
   • A intersect B
6. Draw 3-set Venn diagrams to illustrate each of the following:
   • (B union C)-(A intersect C)
   • (A intersect B)-C
   • (B - C) union (C - B) union A
7. Given A={1,2,4,5,7,9} and B={2,3,4,5,6}, find each of the following:
   • A union B
   • A-B
   • B-A
   • A intersect B