2.2djj.notebook
September 29, 2009
Section 2.2: Subsets Objectives 1­ 3
Subset: Set A is a subset of B, denoted A ⊆ B, if every element of A is also an element of B.
Proper Subset: Set A is a proper subset of B, denoted A ⊂ B, if A is a subset of B and A ≠ B.
ex. C = {2, 4, 6, 8} E = {1, 2, 3, 4}
D = {4, 6} F = {8, 6, 4, 2}
Write ⊆ or ⊈: C _____ D
D _____ E
D _____ C
C _____ F
Write ⊆, ⊂, both, or neither:
C _____ D
D _____ E
D _____ C
C _____ F
Be careful with notations! {4} ∈ {1, 2, 3, 4} True or False
{4} ⊆ {1, 2, 3, 4} True or False
Sep 5­11:35 AM
1
2.2djj.notebook
September 29, 2009
Number of Subsets
If B = {5, 10, 15, 20}, is B a subset of B? ______
is B a proper subset of B? ______
is Φ a subset of B? ______
is Φ a proper subset of B? ______
Every set is a subset of itself and the empty set is a subset of every set! A set having n elements has subsets and proper subsets.
ex. Set B has = 16 subsets and = 15 proper subsets.
Hw. #76: A cheese pizza can be ordered with some, all, or none of the following set of toppings: {beef, ham, mushrooms, sausage, peppers, pepperoni, olives, prosciutto, onion}. How many different variations are available for ordering a pizza?
See text ex. 1 ­ 7. Sep 5­11:39 AM
2
2.2djj.notebook
September 29, 2009
Sep 29­10:26 AM
3