Set Theory
1.0 Set
1.0 Set
A set is a collection of well defined objects i.e. the objects follow a given rule or rules.
Illustration 1. State which of the following are sets and which are not. Provide suitable explanation.
a. Collection of vowels in the alphabet of English language
b.The collection of young people in a city
c.The collection of people below the age of $25$
d.The collection of students who are short
e.The collection of good cricketers
f.The collection of all odd numbers
Solution:
| COLLECTION | CLASSIFICATION |
| a. Collection of vowels in the alphabet of English language | This set is well defined and we know that there are only five of them. |
| b. The collection of young people in a city | This is not a set, as a person who is $60$ years may find $40$ year old people young and $40$ year old man may feel $20$ year old man young. This collection is not well defined and is relative to the person who defines it. |
| c. The collection of people below the age of $25$ in a city | This is a well defined set as the age limit is given. Hence, this is not relative but the same for any one who collects it. |
| d. The collection of students who are short | In this collection, a $6$ feet man may find others around him short, a $4$ feet student may find other kids small. Thus this collection is relative to the one's own height. Hence this is not a set. |
| e. The collection of good cricketers | Opinions vary about a cricketer from person to person. One may find a cricketer good and another may find the same person bad. Hence, this collection is relative to a person's opinion and not the same for everyone.Thus it is not a set. |
| f. The collection of all odd numbers | The odd numbers hold the same definition through out the world. It does not change. Hence universally everyone will form the same set of numbers. Thus, this collection is a set. |
