In maths, a set is a group of objects or elements. It deals with the properties & a collection of objects. Set theory is used in various concepts like fields, loops, groups, abstract algebra constructs, and closed part of one more operations. Here, we can check whether the given objects form a set or not? Get the conditions, and solved example problems in the following segments of this page.
What is a Set?
A set is a collection of objects or elements. The ways of describing sets are statement form, roster form, and set builder form. All the elements of the set are enclosed by curly braces. While forming a set the objects are grouped into a single entity. The example of a set are A = {“apple”, “custard apple”, “pineapple”, “orange”, “banana”, “grapes”, “papaya”}. The essential features of a set theory are along the lines.
- The relationship that may or may not exist between a set and an object is called a membership relationship.
- The principle of extension states that the set is defined by its objects instead of a single or defining group.
How to Confirm that Whether Objects Form a Set?
The following states help the students to check whether the group of objects form a set or not.
- A bunch of “lovely flowers” is not a set. As the object i.e flowers is not well defined. The reason is the word lovely is a relative term. What one person may feel lovely is not the same for other persons.
- A bunch of “red roses” is a set, because every red color rose is included in this set. It means set objects are well defined.
- A group of young actors” does not form a set. Because the particular rage of the young actor is not specified exactly. So, the objects are well defined.
- A group of “employees with age between 20 and 30 years” is a set. Because here the range of age of employees is provided. So, it can easily decide which employee is included and who is excluded.
Also, Read
| Basic Concepts of Sets | Subsets of a Given Set | Subsets | Laws of Algebra of Sets |
| Intersection of Sets | Different Notations in Sets | Union of Sets |
Whether Objects Form a Set or Not Examples
State Whether the Objects Form a Set
Example 1:
The school has 45 students who know Telugu.
Solution:
The given objects form a set.
Reason: It can easily find the number of students in the school who can know the Telugu language by just asking them. Count those students. Hence, the objects form a set.
Example 2:
All the objects are heavier than 35 kg.
Solution:
The given objects form a set.
Every object’s weight is compared. If the weight is more than 28 kgs, then they are selected. It means objects are well defined.
Hence, the objects form a set.
Example 3:
All the number of books in the school bag is 6.
Solution:
The given objects form a set.
Reason: Check every student’s school bag, if the number of books is equal to 6 then take them into consideration. It says that objects are well defined.
Hence, the objects form a set.
Example 4:
All problems of this book, which are difficult to solve.
Solution:
The given objects do not form a set.
The problems one may difficult may not be difficult problems for other students. So, the objects not well defined.
Hence, the objects do not form a set.