Subsets Subsets are sort of like nested Russian

Subsets

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

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

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.

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” ‹

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.

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.

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

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

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} 3 A set with 3 elements has 2 or 8 subsets 3 A set with 3 elements has 2 – 1 or 7 subsets

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

Vocabulary Subset Proper subset Improper subset Empty set