1. Subsets

2. Subsets are sort of like nested Russian dolls: the subset “fits inside” the set.

3. Subsets Set A is a subset of set B if all of the members in set A are also in set B. set A = { 1, 2, 3 } set B = { 1, 2, 3, 4, 5, 6 } Set A is a subset of set B

4. NOT a Subset Set A is NOT a subset of set B if any member in set A is not also in set B. set A = { 1, 2, 9 } set B = { 1, 2, 3, 4, 5, 6 } Set A is NOT a subset of set B because of the 9.

5. Proper Subsets If set A has fewer elements than set B, it is called a proper subset and we use The idea is very similar to the concept of “less than” ‹

6. Improper Subsets If they are the same set, it is called an improper subset and we use (or we could use =). By definition, every set is a subset of itself.

7. Generic Subsets If we aren’t sure if it’s a proper subset or an improper subset, we use the generic subset symbol. That way it is true either if it is proper or improper.

8. The Empty Set Also by definition: The empty set is a subset of every other set. For every set A:

9. Listing Subsets Let’s list all the subsets of the set {1, 2} The proper subsets: {1}, {2}, and The improper subset: {1, 2} A set with 2 elements has 2 2 or 4 subsets A set with 2 elements has 2 2 – 1 or 3 proper subsets

10. Listing Subsets Let’s list all the subsets of the set {1, 2, 3} The proper subsets: {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3} The improper subset: {1, 2, 3} A set with 3 elements has 2 3 or 8 subsets A set with 3 elements has 2 3 – 1 or 7 subsets

11. Number of Subsets If a set has n elements The number of subsets will be 2 n The number of proper subsets will be 2 n – 1

12. Vocabulary Subset Proper subset Improper subset Empty set