Question

A basketball team has three substitute players: Jordan, Frazier, and Drexler. The coach can choose to use some or none, but not all, of these substitute players in a game. List all the possible sets of substitute players that the coach can use in roster form.

Answer 1

• {Jordan, Frazier}
• {Frazier, Drexler}
• {Jordan, Drexler}
• {Jordan}
• {Frazier}
• {Drexler}
• { }

There are 7 subsets listed above. A subset is where we form a smaller set consisting of people from the original set. The first three subsets are when the coach picks 2 players in any order. Order doesn't matter in a set. The next three subsets are known as singletons. The last subset is the empty set. The empty set is a subset of any set.

The empty set is the set with nothing inside it. Not even the value 0 is inside it. We write a pair of curly braces here. Or we could use the special symbol
`\varnothing` to represent the empty set.

Notice how the original set has n = 3 people in it. There would be 2^n = 2^3 = 8 different subsets (the entire collection of which is known as the power set). Subtract off 1 to remove the original set itself and we'll have 8-1 = 7 proper subsets.