Sets, Notations and Language :Home assignment
By: Yashika P
Roll no. 28 Sets, Notations and Language
Slide 2:A set is a collection of distinct objects
Slide 3:The members of a set are often called elements. The elements are represented in { }.
There are two ways of describing the elements of the set.
First way → Set-builder form
Second way → Roster form
Set-builder form :Set-builder form Examples:
A is the set whose members are the first four positive integers. (1,2,3,4)
A = {x:x is a positive integer, x ≤ 4}
Read it as “Set of all x such that x is a positive integer, x less than or equal to 4”
Roster form :Roster form Examples:
B is the set of colors of the French flag.
B = {blue, white, red}
The elements in a set should NOT repeat.
The elements in a set can be written in ANY order.
The elements are represented by: :The elements are represented by: Elements are represented by ∈
Example – if 2 is an element of J, it could be represented as:
2 ∈ J
If 8 is not an element of R, it could be represented as:
8 ∉ R
Universal set :Universal set Universal set is the set which has all the elements.
Example:
A = {blue, black, brown, red}
B = {1, 3, 5, 7, 9}
The universal set has all of the elements in the above sets and it could even have other elements.
Null set :Null set The set in which there are no elements is called a null set.
It could be represented as:
A = { }
OR
A = Ø
Subset and Superset :Subset and Superset Given two sets, A and B, all the elements of set A are in set B but set B has some extra elements, then set A is called as a subset of B and set B is called the superset of A.
Every set is a subset of itself.
Null set is a subset of all the sets.
All the sets are subsets of the universal set.
Subsets and supersets :Subsets and supersets Examples:
A = {1, 2, 4, 5}
B ={6,2,3,1,4,5,7,9}
B contains A or B is a superset of A or A is a subset of B
A ⊂ B or B ⊃ A
Union :Union When two sets are combined, it is known as a union.
Example:
R = {2, 4, 5, 3, 88}
G = {red, blue, yellow, green}
R ∪ G = {2, 4, 5, 3, red, green, blue, 88, yellow}
‘∪’ is the notation of union
Union should NOT be confused with universal set as union cannot contain any extra element other than the ones in the subsets.
Intersection :Intersection A new set can be constructed by determining which members two sets have "in common".
Example:
A = {1, 43, 72, 101, 708, 52, 9, 4, 66, 193}
B = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A ∩ B = {1, 9, 4}
‘∩’ is the notation for intersection
Difference :Difference The difference between two sets could be found out by finding the elements in the first set which are not there in the second set (first set – second set) or vice versa (second set – first set)
Example:
A = {2, 3, 4, 5, 6, 7, 8, 9}
B ={1,4, 7, 10, 33, 43, 66}
A – B = {2, 3, 5, 6, 8, 9}
B – A = {1, 10, 33, 43, 66}
A – B ≠ B – A
Complement :Complement Complement are elements of the given universal set which are not present in the set.
Examples:
A = {5, 6, 7, 8, 9}
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Ac = {1, 2, 3, 4}
Venn Diagrams :Venn Diagrams Venn diagrams are used to represent sets. Intersection A is a subset of B
Venn diagrams :Venn diagrams Union Difference Complement Intersection