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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}