1. Note that the subsets of {a} are Ø and {a}. No matter how you list them, they fit the rule. Now try working with the subsets of a two-element set. (These problems are suggested in the Warm Up Problems.)
2. See if you can use a sequence of subsets for an (n-1)-element set to obtain a sequence for an n-element set. For example:

   Subsets of {a}: Ø, {a}
   Subsets of {a, b}: Ø, {a}, {b}, {a, b}
   

   The second sequence doesn’t fit the rule; can you “build off” the first sequence in some way that helps you rearrange the second sequence so that it will fit the rule? Once you do that, can you use a similar technique on the (rule-fitting) second sequence to create a list for {a, b, c} that works?

3. Draw a picture where each subset is connected by an edge to all of the subsets it could move to next. For example, from the subset {b} of {a, b, c}, one can move to the sets Ø, {a, b}, and {b, c}; the picture might look like this:
   

   In this picture, moving down gives you a subset (one element is removed) and moving up gives you a superset (one element is added). Try to extend this picture to include all of the subsets of {a, b, c}. How can you use this diagram to produce a sequence of subsets that follow the rules?

Subsets in Sequence Project Description |
Prerequisites | Warm Up Problems | Hints |
Resources | Teaching Notes | Extensions |
Results Making Mathematics Home |
Mathematics Projects | Students | Teachers |
Mentors | Parents | Hard Math Café |