1. Set Concepts & Subsets
Sections 2.1 & 2.2

2. Set A is equivalent to set B means that set A and set B contain the same number of elements. Ex: A = {1, 4, 7, 8, 10} B = {January, February, March, April, May} n(A) = n(B), so set A is equivalent to set B
Equivalent Sets

3. Set A is equal to set B means that set A and set B contain exactly the same elements, regardless of the order. Ex: A = {a, b, c, d} B = {b, c, a, d} A and B are equal sets, so we say A = B
Equality of Sets

4. Set A is a subset of set B, expressed as A ⊆ B, if every element in A is also an element in B. Ex: A = {1, 2, 3, 4, 5} B = {1, 2, 3, 4, 5, 6, …} A ⊆ B since every element in A is an element in B
Subset of a Set

5. Set A is a proper subset of set B, expressed as A ⊂ B, if set A is a subset of set B and sets A and B are not equal (A ≠ B) Ex: A = {1, 2, 3, 4, 5} B = {1, 2, 3, 4, 5, 6, …} A ⊂ B since there are elements in B that are not in A
Proper Subset of a Set

6. Empty Set Properties For any set A, ∅⊆ A
For any set B other than the empty set, ∅⊂ A
Empty Set Properties

7. The number of subsets of a set with n elements is 2n Ex: G = { a, b, c, d, e} # of subsets =

8. Number of Proper Subsets
The number of proper subsets of a set with n elements is 2n - 1 Ex: G = { a, b, c, d, e} # of proper subsets =
Number of Proper Subsets

9. Homework  Page 54 (84 – 88 all) Page 63 (6 – 14, 26 – 34,
48 – 54, 62 – 68 evens)
Homework 