For any set B

2.2 Subsets.
Section 2.2 Notes Page 1
Set A is a subset of set B, expressed as A⊆B, if every element in set a is also an element in set
B. (The notation A⊈B means that A is not a subset of B)
Set A is a proper subset of set B, expressed as A⊂B, if set A is a subset of set B and set A and
B are not equal.
For any set B, ∅ ⊆ 𝐵.
For any set B other than the empty set, ∅ ⊂ 𝐵.
The number of subsets of a set with n elements is 2𝑛
The number of proper subsets of a set with n elements is 2𝑛 − 1
Ex1. Write ⊆ or ⊈ in each blank to form a true statement:
a) A = {3, 5, 7}, B = {1, 3, 5 7, 9 11}
A_____B
b) A = {X|X is a letter in the word proof}, B = {Y|Y is a letter in the word roof} A ____ B
c) A = {X|X is a day of the week}, B= {Monday, Tuesday, Wednesday, Thursday, Friday,
Saturday, Sunday}
A ____ B
Ex2. Write ⊆, ⊂, or both, in each blank to form a true statement:
a) A = {X|X is a person and x lives in San Francisco}, B = {Y|Y is a person and x lives in
California}
A ____ B
b) A = { 2, 6, 8}, B = {2, 8, 4, 6}
A _____ B
Ex3. Let A = { } and B = {6, 7, 8}. Is A⊆B?
Section 2.2 Notes Page 2
Ex4. Finding the number of distinct subsets and the number of distinct proper subsets for each
set:
a) { a, b, c, d, e}
b) {X|X is nature numbers and 9≤X≤15}