Set, notation and language

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