The document defines sets and describes their key characteristics and operations. It defines a set as a collection of distinct objects, and outlines different types of sets including empty, finite, infinite, subset, disjoint, equal, union, and intersection sets. It also explains Venn diagrams and common set operations such as union, intersection, and complement. Finally, it lists several laws of sets including commutative, associative, idempotent, distributive, and De Morgan's laws.

1. SETS
Submitted to
Md. Auhidur Rahman
Lecturer
Institute of Information & Technology
Presented by
Nadim Bhuiyan(ASH1825034M)
Saifur Rahman(ASH1825031M)
Fazle Rabbi(ASH1825004M)
Mahabub (ASH1825003M)

2. Contents
 Definition of Sets
 Kinds of sets
 Venn Diagrams
 Operation on sets
 Laws of sets

3. Definition of sets:
 A set is a simply well defined list or collection distinct objects.The objects in a set is called
element or member of the set.
 A set is an abstract data type that can store certain values,without any particular order,
and no repeated values,
 A set is a group or collection of objects or number considered as an entity unto itself.
 For Example:
• a set of chairs,
• the set of nobel laureates in the worlds,
• the set of integers,
• the set of natural numbers less than 10,
• the set of books in the table.

4. Kinds of sets
Empty Set
Finite Set
Infinite Set
Sub Set
Disjoint Set
Equality Set
Union Set
Intersection Set

5.  Disjoint Set: Two set are called disjoint if their intersection is the empty set.
let A and B be the set,then the disjoint set is A ∩ B= { }
 Equal set: Two set A and B are said to be equal or A=B if and only if A ⊆ B.
and B ⊆ A .
let A and B the set ,then the equal set is ,A={1,2,3,4,5} B={1,2,3,4,5}
 Union Set: The union of two sets A and B is the set of all elements belonging
to A or B or both.
let A and B the set ,then the union set is A U B.

6.  Empty set: Any set that has no element in it is called an empty
set or null set.
let, A is a set then we denote it empty set A= Ø or { }
 Finite set: A set is called finite if it’s elements are equal in
number to some specifiable nonnegative integers.
let,A is a set ,then finite set A={2,3,4,5,6}
 Infinite set: A set is called infinite if the number of it’s elements
is greater than any positive integer.
let,A is a set ,then finite set A={2,3,4,5,6…….}
 Sub set: If every element of the set A is also an element of the
B. Then A is said to be a sub set of B.
let A and B the set , A is a subset of B, denoted by A ⊆ B.
•

7. Venn Diagrams
A helpful scheme to illustrate the relationship between sets and set operation
is the Venn Diagram.

8. Operation on Sets
Union,U.
 AUB is the set of all elements that are in A OR B.
Intersection ∩ .
 A ∩ B is the set of all elements that are in A AND B.

9. Operation of sets
Complement
 A is the set ,we denoted it A’ or A∁ .

10. Laws of sets
1. Commutative Laws:
• For any two finite sets A and B;
(i) A U B = B U A
(ii) A ∩ B = B ∩ A
2. Associative Laws:
• For any three finite sets A, B and C;
(i) (A U B) U C = A U (B U C)
(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C)

11. Laws of sets
3. Idempotent Laws:
• For any finite set A;
(i) A U A = A
(ii) A ∩ A = A
4. Distributive Laws:
• For any three finite sets A, B and C;
(i) A U (B ∩ C) = (A U B) ∩ (A U C)
(ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C)
5.De Morgan’s Laws :
For any three finite sets A, B ;
(i) (A U B)’ = A' ∩ B'
(ii) (A ∩ B)’ = A' U B'