This document provides an overview of sets as presented by Muhammad Saad. It defines what a set is, including that a set is a collection of distinct objects and examples of finite and infinite sets. It discusses empty or null sets, equal sets, subsets, union, intersection, difference, complement, and partition of sets. The key topics covered are the definition of a set, examples of different types of sets, and basic set operations like union, intersection, difference, and complement.

1. Name : Muhammad Saad
Roll no: 107
Sec : A
Subject :Discrete Structure
Topic of presentation:
Sets

2. Introduction
O The theory of sets was developed by German
mathematician Georg Cantor (1845-1918).
O He first encountered sets while working on
“problems on trigonometric series”.
O Studying sets helps us categorize information. It
allows us to make sense of a large amount of
information by breaking it down into smaller
groups.

3. Sets
O Sets are used to define the concepts of
relations and functions. The study of
geometry, sequences, probability, etc.
requires the knowledge of sets.

4. O Definition: A set is any collection of objects specified in
such a way that we can determine whether a given object
is or is not in the collection.
O In other words A set is a collection of objects.
O These objects are called elements or members of the set.
O The symbol for element is .
O For example, if you define the set as all the fruit found in
my refrigerator, then apple and orange would be elements
or members of that set.
O The following points are noted while writing a set.
O Sets are usually denoted by capital letters A, B, S, etc.
O The elements of a set are usually denoted by small letters
a, b, t, u, etc.

5. FINITE AND INFINITE SETS
O A set is finite if it consists of a definite number of
different elements ,i.e., if in counting the different
members of the set, the counting process can
come to an end, otherwise a set is infinite.
O Example: {1, 2, 3, 4, 5} , {1, 2, 3, 4,………..up to 100}
O If P be the set of all points on a line between the
distinct points A and B ,then P is infinite
O or {2, 4, 6, 8, 10,…………………. } set of even
numbers

6. Empty or Null Set
O A set that contains no members is called
the empty set or null set.
O Set with no elements.
O { } or Ø.
O Examples: Let A = {x : 9 < x < 10, x is a
natural number} will be a null set because
there is NO natural number between
numbers 9 and 10.

7. Equal Sets
OEqual sets are sets which have the
same members. For example, if
OP ={1,2,3},Q={2,1,3},R={3,2,1}
Othen P=Q=R.

8. Subset
OSets which are the part of another
set are called subsets of the original
set.
O For example, if A={1,2,3,4} and B ={1,2}
then B is a subset of A.
Oit is represented by "⊆“.

9. Union Set
O Union of two sets A and B is the set of all
elements in either set A or B.
O Written A B.
O A B = {x | x A or x B}
O Example {a, b, c}  {2, 3} = {a, b, c, 2, 3}

10. Intersection
O Intersection of two sets A and B is the set
of all elements in both sets A or B.
O Written A B.
O A B = {x | x A and x B}

11. Difference Set
O Difference of two sets A and B is the set
of all elements in set A which are not in
set B.
O Written A - B.
O A - B = {x | x A and x B}
O also called relative complement.

12. Complement Set
O Complement of a set is the set of all elements not
in the set.
O Written Ac
O Need a universe of elements to draw from.
O Set U is usually called the universal set.
O Ac = {x | x U - A }

13. Partition Set
O Partition - A collection of disjoint sets
which collectively
O Make up a larger set.
O Ex: Let A = {a,b}; B = {c,d,e}; C = {f,g} and
O D = {a,b,c,d,e,f,g}
O Then sets A,B,C form a partition of set D

14. Thank You