Algebra Know-It-ALL

7. What is the intersection of these two sets? What is their union?

A= {1, 1/2, 1/3, 1/4, 1/5, 1/6, ...}

G= {1, 1/2, 1/4, 1/8, 1/16, 1/32, ...}

In set A, the denominator of the fraction increases by 1 as you go down the list. In set G,

the denominator doubles as you go down the list. All the numerators in both sets are

equal to 1.

8. List all the subsets of {1, 2, 3}. Here’s a hint: Whenever you want to find all the subsets
   of a small set like this, first list its individual elements. Then make up every possible set
   that contains at least one of those elements. Finally, be sure to include the empty set,
   which is a subset of any other set.


9. List all the subsets of {1, {2, 3}}. Be careful. The hint given with Problem 8 is important
   here.


10. List all the subsets of {1, {2, {3}}}. Be extra careful! The hint given with Problem 8 is
    even more important here.

34 The Language of Sets

Universe

A

B

C

D

E

P

Q

Figure 2-6 Illustration for Probs. 3 and 4.