Research Problem...

Subsets in Sequence...

An investigation into changing places...

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The set {a, b, c} has exactly eight subsets.
1). List all the subsets of {a, b, c}.
2). Now arrange those subsets in a sequence so that each subset in the sequence differs from the one before it in one of two ways:
One new element is inserted: Example 1: {a}, {a, b} Example 2: {a, b}, {a, b, c}
One old element removed Example 1: {a, b, c}, {a, c} Example 2: {b}, Ø
3). Can you create more than one sequence that fits these criteria?
4). Create a listing like this for the subsets of {a, b, c, d}.
5). Describe a general method (or explain why there isn’t one) for creating such a sequence of the subsets of any set {a1, a2, a3, ...an}.