√ Definition of Sets and Examples of Set Statistical Problems (Complete)
Definition of Sets and Examples of Set Statistical Problems (Complete) – Before knowing how to set examples of statistical problems. The following is the definition of the set. Sets are the basic concept of all branches of mathematics. The father of set theory is Gerorg Cantor.
Definition of Sets and Examples of Set Statistical Problems (Complete)
A set is a collection or a collection of objects from our intuition or thoughts that can be distinguished from one another. The objects in a set are called elements, elements, or members. Sets are symbolized by capital letters of the alphabet, for example: A, B, …, Z.
For Example: The set of the first five positive even numbers: B = {4, 6, 8, 10}. If x is a member of the association A, then written x Î A. And if x not a member of the set A, then written x Ï A There are 4 ways to define a set, namely:
- Register all its members
- State the characteristics possessed by its members.
- Declare properties with patterns
- Use set builder notation.
Types of Associations based on the Number of Members
When viewed from the types of sets based on the number of members, the sets can be divided into two, namely, the empty set and the universal set. There is an explanation as follows:
-
Empty set, which is a set that has no members. Denoted by “ ” or { }.
Example: even prime number > 10 -
Universe set, which is the set whose members are all objects of discussion. The universal set is denoted by S or U.
Example: S = {-4, 5, 7, 9} and A = {7, 9} then S is the universe of set A
Finite set And infinite set. A set is said to be finite if it has a finite number of elements. A set is said to be infinite if it has an infinite number of members.
Example: H = {x | x= 1, 2, 3, 4, 5, 6, …}, H is called an infinite set.
A = {x| x= 1, 2, 3, 4, …, 10}, A is called a finite set.
Section set (Subsets). Set A is said to be a subset of set B written "A⊂B”, if each member of A is a member of B.
Example: A = {2, 3, 5} and B = {1, 2, 3, 4, 5}. Then A⊂B.
P = {2, 3, 5, 7} and Q = { 1, 3, 5, 7, 9}. Then P⊄Q
Two sets A and B are said to be equal, written “A=B”, if and only if A⊂B and B⊂A.
Example: A = {2, 3, 5,7} and B = {2, 3, 5, 7}. Then A=B.
Intersecting set. Two sets A and B are said to intersect, written "A∝B" if and only if there are elements that are members of B.
Example: A = {2, 3, 5,} and B = {1, 3, 5, 7, 9}. Then A∝B.
Loose set. Two sets A and B are said to be separated by writing "//" if and only if the two members of the sets are non-empty and do not have the same members.
Example: A = {3, 5, 7,11} and B = {2, 4, 6, 8}. Then A ∕∕ B.
Operations on a set
There are 5 operations in a set, namely:
- Combined (Union). Given sets A and B. The union of sets A and B written with A∪B is a set whose members consist of either members of A or members of B, or members of both. So A∪B={x | x∈A or x∈B}.
- Intersection. Given sets A and B. The intersection of sets A and B written with A∩B is a set whose members consist of both members of A and members of B. So A∩B = { x | x ∩ A and x ∩B }
- Complement. Given a set A. The complement of A is written as “Ac or A' " is a set whose members are in the universal set but are not members of A. So Ac ={x ┤| x∈S, x∉A}
- Differentiate the two sets. The difference between two sets A and set B written "A-B" or "A∩B^c" is a set whose members consist of A and are not members of B. So A-B={x | x∈A and x∉B}.
- The sum of the two sets. The sum of two sets A and set B written "AÅB" is a set whose members consist of members of A who are not members of B and members of B who are not members of A. So AÅB={x |x∈(A-B) or x∈(B-A)}.
Thus our discussion this time about Definition of Sets and Examples of Set Statistical Problems (Complete), hopefully it can be useful for all of us. Thank you 🙂
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