PPT - Set Theory | Quantitative Aptitude for CA Foundation PDF Download

 Page 1


SET THEORY 
? Set: A collection of well defined objects. 
? Sets are usually denoted by capital letters A, B, C 
etc. and their elements are denoted by a, b, c etc. 
? Few examples: 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. a,e,i,o,u. 
? The set of 3 cycle companies of India. This set 
contains 3 elements i.e. Hero, Avon, Suncross. 
? The set of 4 rivers in India. This set contains 4 
elements i.e. Ganga, Yamuna, Beas, Narmada, 
Kaveri. 
? The collection of good cricket players of India is 
not a set 
 
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SET THEORY 
? Set: A collection of well defined objects. 
? Sets are usually denoted by capital letters A, B, C 
etc. and their elements are denoted by a, b, c etc. 
? Few examples: 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. a,e,i,o,u. 
? The set of 3 cycle companies of India. This set 
contains 3 elements i.e. Hero, Avon, Suncross. 
? The set of 4 rivers in India. This set contains 4 
elements i.e. Ganga, Yamuna, Beas, Narmada, 
Kaveri. 
? The collection of good cricket players of India is 
not a set 
 
REPRESENTATION OF A SET 
Roster 
Form 
Set Buider 
Form 
 
Page 3


SET THEORY 
? Set: A collection of well defined objects. 
? Sets are usually denoted by capital letters A, B, C 
etc. and their elements are denoted by a, b, c etc. 
? Few examples: 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. a,e,i,o,u. 
? The set of 3 cycle companies of India. This set 
contains 3 elements i.e. Hero, Avon, Suncross. 
? The set of 4 rivers in India. This set contains 4 
elements i.e. Ganga, Yamuna, Beas, Narmada, 
Kaveri. 
? The collection of good cricket players of India is 
not a set 
 
REPRESENTATION OF A SET 
Roster 
Form 
Set Buider 
Form 
 
ROSTER FORM 
? This method is also called Tabular Method. 
? In this, a set is described by listing elements, 
separated by commas, within braces { } 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. {a,e,i,o,u } 
? If A is the set of even natural numbers, then              
A = {2, 4, 6, …….. } 
? If A is the set of all prime numbers less than 11, then 
A = {2, 3, 5, 7} 
? Note: 
? The order of writing the elements of a set is 
immaterial. 
? An element of a set is not written more than once. 
  
Page 4


SET THEORY 
? Set: A collection of well defined objects. 
? Sets are usually denoted by capital letters A, B, C 
etc. and their elements are denoted by a, b, c etc. 
? Few examples: 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. a,e,i,o,u. 
? The set of 3 cycle companies of India. This set 
contains 3 elements i.e. Hero, Avon, Suncross. 
? The set of 4 rivers in India. This set contains 4 
elements i.e. Ganga, Yamuna, Beas, Narmada, 
Kaveri. 
? The collection of good cricket players of India is 
not a set 
 
REPRESENTATION OF A SET 
Roster 
Form 
Set Buider 
Form 
 
ROSTER FORM 
? This method is also called Tabular Method. 
? In this, a set is described by listing elements, 
separated by commas, within braces { } 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. {a,e,i,o,u } 
? If A is the set of even natural numbers, then              
A = {2, 4, 6, …….. } 
? If A is the set of all prime numbers less than 11, then 
A = {2, 3, 5, 7} 
? Note: 
? The order of writing the elements of a set is 
immaterial. 
? An element of a set is not written more than once. 
  
SET BUILDER FORM 
? This form is also called Property Form.  
? In this, a set is represented by stating all the 
properties P(x) which are satisfied by the 
elements x of the set and not by other element 
outside the set. 
? If A is the set of even natural numbers, then 
 A = {x: x ? N, x = 2n, n ? N} 
 A = {x: x is a natural number and x = 2n for n ? N} 
? If A = {0, 1, 4, 9, ……} 
 A = {x
2 
: x ? N} 
? If B = The set of all real numbers greater than -3 and 
less than 3   
 B = {-3<x<3 : x ? R} 
 
 
 
Page 5


SET THEORY 
? Set: A collection of well defined objects. 
? Sets are usually denoted by capital letters A, B, C 
etc. and their elements are denoted by a, b, c etc. 
? Few examples: 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. a,e,i,o,u. 
? The set of 3 cycle companies of India. This set 
contains 3 elements i.e. Hero, Avon, Suncross. 
? The set of 4 rivers in India. This set contains 4 
elements i.e. Ganga, Yamuna, Beas, Narmada, 
Kaveri. 
? The collection of good cricket players of India is 
not a set 
 
REPRESENTATION OF A SET 
Roster 
Form 
Set Buider 
Form 
 
ROSTER FORM 
? This method is also called Tabular Method. 
? In this, a set is described by listing elements, 
separated by commas, within braces { } 
? The collection of vowels in English alphabets. This 
set contains five elements i.e. {a,e,i,o,u } 
? If A is the set of even natural numbers, then              
A = {2, 4, 6, …….. } 
? If A is the set of all prime numbers less than 11, then 
A = {2, 3, 5, 7} 
? Note: 
? The order of writing the elements of a set is 
immaterial. 
? An element of a set is not written more than once. 
  
SET BUILDER FORM 
? This form is also called Property Form.  
? In this, a set is represented by stating all the 
properties P(x) which are satisfied by the 
elements x of the set and not by other element 
outside the set. 
? If A is the set of even natural numbers, then 
 A = {x: x ? N, x = 2n, n ? N} 
 A = {x: x is a natural number and x = 2n for n ? N} 
? If A = {0, 1, 4, 9, ……} 
 A = {x
2 
: x ? N} 
? If B = The set of all real numbers greater than -3 and 
less than 3   
 B = {-3<x<3 : x ? R} 
 
 
 
TYPES OF SETS 
? Empty Set: A set is said to be empty or null or void 
set if it has no element and it is denoted by f. 
? In Roster Method, it is denoted by {  } 
? Examples:  
? A = {x: x ? N,  7 < x < 8} = f 
? B = {x ? R : x
2
 = -2} = f  
?C = Any Indian company which is into Automobiles, 
Clothing, Plastics, Paper, Processed Food  
 
? Note:  
? {f} is not a null set, since it contains f as an element. 
? {0} is not a null set, since it contains 0 as an element. 
 
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