UNIT-1 SET THEORY
Overview
This chapter deals with the concept of set, operations on sets. Concept of sets will be
Useful in studying the relations and functions.
The empty set A set which does not contain any element is called the empty
set or the void set or null set and is denoted by { } or f.
Finite and infinite sets A set which consists of a finite number of elements is
called a finite set otherwise, the set is called an infinite set (A A A A
Subsets A set A is said to be a subset of set B if every element of A is also an
element of B. In symbols we write A Ì B if a Î A Þ a Î B.
We denote set of real numbers by R
set of natural numbers by N (A B C D) (A), (B), (C)
set of integers by Z
set of rational numbers by Q
set of irrational numbers by T
We observe that
N Ì Z Ì Q Ì R,
T Ì R, Q Ë T, N Ë T
Equal sets Given two sets A and B, if every elements of A is also an element of
B and if every element of B is also an element of A, then the sets A and B are said to
be equal. The two equal sets will have exactly the same elements
Intervals as subsets of R Let a, b Î R and a < b. Then
(a) An open interval denoted by (a, b) is the set of real numbers {x : a < x < b}
(b) A closed interval denoted by [a, b] is the set of real numbers {x : a £ x £ b)
Power set The collection of all subsets of a set A is called the power set of A.
It is denoted by P(A). If the number of elements in A = n , i.e., n(A) = n, then the
number of elements in P(A) = 2n.
Universal set This is a basic set; in a particular context whose elements and
subsets are relevant to that particular context. For example, for the set of vowels in
English alphabet, the universal set can be the set of all alphabets in English. Universal
set is denoted by U. A= (1,2,3,4,5,7,8) B= (7,8,9) FIND AUB? SOL= (1,2,3,4,5,7,8,9)
Venn diagrams Venn Diagrams are the
diagrams which represent the relationship between
sets. For example, the set of natural numbers is a
subset of set of whole numbers which is a subset of
Overview
This chapter deals with the concept of set, operations on sets. Concept of sets will be
Useful in studying the relations and functions.
The empty set A set which does not contain any element is called the empty
set or the void set or null set and is denoted by { } or f.
Finite and infinite sets A set which consists of a finite number of elements is
called a finite set otherwise, the set is called an infinite set (A A A A
Subsets A set A is said to be a subset of set B if every element of A is also an
element of B. In symbols we write A Ì B if a Î A Þ a Î B.
We denote set of real numbers by R
set of natural numbers by N (A B C D) (A), (B), (C)
set of integers by Z
set of rational numbers by Q
set of irrational numbers by T
We observe that
N Ì Z Ì Q Ì R,
T Ì R, Q Ë T, N Ë T
Equal sets Given two sets A and B, if every elements of A is also an element of
B and if every element of B is also an element of A, then the sets A and B are said to
be equal. The two equal sets will have exactly the same elements
Intervals as subsets of R Let a, b Î R and a < b. Then
(a) An open interval denoted by (a, b) is the set of real numbers {x : a < x < b}
(b) A closed interval denoted by [a, b] is the set of real numbers {x : a £ x £ b)
Power set The collection of all subsets of a set A is called the power set of A.
It is denoted by P(A). If the number of elements in A = n , i.e., n(A) = n, then the
number of elements in P(A) = 2n.
Universal set This is a basic set; in a particular context whose elements and
subsets are relevant to that particular context. For example, for the set of vowels in
English alphabet, the universal set can be the set of all alphabets in English. Universal
set is denoted by U. A= (1,2,3,4,5,7,8) B= (7,8,9) FIND AUB? SOL= (1,2,3,4,5,7,8,9)
Venn diagrams Venn Diagrams are the
diagrams which represent the relationship between
sets. For example, the set of natural numbers is a
subset of set of whole numbers which is a subset of
