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This symbol 符号 means “is a subset 子集of"
AB
This is read "A is a subset of B". B = {1, 2, 3, 4, 5}
A = {1, 2, 3}
If a set doesn„t contain any elements it is called the empty set 空集 or the null set. It is denoted by ቤተ መጻሕፍቲ ባይዱor { }. NOT {}
SETS
A = {1, 3, 2, 5} n(A) = | A | = 4
（集合）
Sets are denoted by Capital letters （大写字母） Sets use “curly” brackets
（花括号，大括号）
The number of elements （元素） in Set A is 4
AB=
There are no elements in both A and B. When this is the case they are called disjoint sets 不相交集合.
Universal Set
A A
B A`
A‵
This means the complement补集 of A, and means the set of all elements in the universal set that are not in A.
Total Number of Possible Subsets 2 4 8
3. {A , B , C}
4. {A , B , C, D}
? 16
The number of possible subsets of a set of size n is ? n
2
A = {1, 2, 3, 4, 5} B = {1, 3, 5, 7, 9}
It is agreed that the empty set is a subset of all other sets so:
A where A is any set.
List all of the subsets of {1, 2, 3}.
{1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3}
universal set is 100 people surveyed
C 40
12
D 24
24
Since 24 did not own a dog or cat, there must be 76 that do.
Set C is the cat owners and Set D is the dog owners. The sets are NOT disjoint. Some people could own both a dog and a cat. Counting Formula: n(A B) = n(A) + n(B) - n(A B)
AB
= {1, 3, 5}
This is the intersection 交集 symbol. It means the set containing all elements that are in both A and B.
These sets can be visualized with circles in what is called a Venn Diagram.韦恩图
AB
= {1, 2, 3, 4, 5, 7, 9}
Remember we do not list elements more than once.
This is the union 并集 symbol. It means the set that consists of all elements of set A and all elements of set B.
Notice the empty set is NOT in set brackets.
Number of Elements in Set 1. {A} 2. {A , B}
Possible Subsets {A} {A , B} {A} {B} {A , B , C} {A , B} {A , C} {B , C} {A} {B} {C} {A , B , C , D} {A , B , C} {A , B , D} {A , C , D} {B , C , D} {A , B} {A , C} {A , D} {A , B} …… {D}
n(C D) = 76
This n means the number of elements in the set
A A
B B
A
B
AB
Everything that is in A or B.
AB
Everything that is in A AND B.
Often will have a set that contains all elements that we wish to consider. This is called the universal set 全集. All other sets are subsets of this set.
100 people were surveyed. 52 people in a survey owned a cat. 36 people owned a dog. 24 did not own a dog or cat. Draw a Venn diagram.
52 + 36 = 88 so there must be 88 - 76 = 12 people that own both a dog and a cat.
3 A
7A
7 is not an element of A
3 is an element of A
A set is a distinct collection of objects. The objects are called elements. Order 顺序 does not matter. If a set {1, 2, 3, 4} = {2, 3, 1, 4} contains 包含 the same elements as another set, the sets are equal. {1, {1, {1,2,2,2,5,5} 3, 3,3,3,5} 2} In never repeat elements in Weascending order 大小顺序 a set.
