- What is Set Theory?
- Illustrated Examples of Set Theory
- FAQs on Set Theory
What is Set Theory?
A well-defined collection of objects is known as a set. The members of a particular set are known as the elements of the set. There is no limit on the number of elements of a set. The elements in a set can be ordered in any manner, and the set remains the same.
Representation of Sets:
A capital alphabet denotes a set’s name while a lower case letter indicates the elements or objects in it. Greek letter epsilon represents ‘belongs to’ in a set.
If M is a set and m1, m2, m3, ... are the members of the set M,
then this can be represented as m1 M.
There are two ways to represent complete sets—the roster form and the set builder form.
- Roster form:
This tabular form of set representation lists all members of the set in curly braces {}, separated by commas. For example- M= {p, q, r, s, t}.
- Set builder form:
The set builder form uses the common property of the members of a set to represent them symbolically. For example- M= {p : p is a prime number}.
Symbols of Set Theory:
Z: Z represents the set of all integers. Z+ symbolises the set of positive integers and Z- symbolises the set of negative integers.
N: N represents the set of all the natural numbers.
Q: Q symbolises the set of all rational numbers.
R: R symbolises the set of all real numbers.
C: C symbolises the set of all complex numbers.
Operations on Sets:
Some operations that are performed on sets are-
- Union of sets
- Intersection of sets
- Set difference
- Symmetric difference
- Complement of sets
- Power set
- Cartesian product of sets
Importance and Weightage
The topic “set theory” is a part of the chapter “Sets” in the syllabus of class 11 maths. This chapter holds a weightage of around 8 marks in the examinations. The knowledge of set theory is crucial to understand “Relations and Functions,” which is a part of the syllabus of class 12 maths.
Illustrated Examples of Set Theory
1. Assume that P (M) = P (N). Show that M = N.
Solution:
To show that M = N
According to the question, P (M) = P (N)
Let x be an element of set M,
x ∈ M.
Since P (M) is the power set of set M, it has all the subsets of set M.
M ∈ P (M) = P (N)
Let K be an element of set N
For any K ∈ P (N),
We have, x ∈ K, K ⊂ N
∴ x ∈ N, ∴ M ⊂ N
Similarly, we have, N ⊂ M
If M ⊂ N and N ⊂ M
∴ M = N.
2. Using properties of sets, show that: M ∪ (M ∩ N) = M.
Solution:
We know that,
M ⊂ M, M ∩ N ⊂ M
∴ M ∪ (M ∩ N) ⊂ M (i)
Also, according to the question,
M⊂ M ∪ (M ∩ N) (ii)
Hence, from equation (i) and (ii)
M ∪ (M ∩ N) = M.
FAQs on Set Theory
Q: Who introduced the concept of sets?
Q: What is an empty set?
Q: How can we represent positive and negative rational numbers? What does the symbol represent?
Q: How are sets represented with the help of Venn diagrams?
Q: What is the application of sets?
Maths Sets Exam
Student Forum
Answered a week ago
Aspirants who wish to pursue a career in the Pharmaceuticals industry must have the following skill-sets:
- Medicinal and scientific research skills
- Communication skills and interpersonal skills
- Adaptation ability
- Therapeutic and counselling skills
- Medical writing and ethics
- Business skills such as marketin
A
Contributor-Level 10
Answered a week ago
The skill sets required for a career in Ground Staff services are as follows:
Communication Skills: Clear and effective communication with passengers and team members.
Customer Service: Providing assistance and addressing passenger queries or issues.
Problem-solving: Ability to handle unexpected situat
A
Contributor-Level 7
Popular Courses After 12th
Exams accepted
CA FoundationExams accepted
ICSI ExamExams accepted
BHU UET | GLAET | GD Goenka TestBachelor of Business Administration & Bachelor of Law
Exams accepted
CLAT | LSAT India | AIBEExams accepted
IPMAT | NMIMS - NPAT | SET
Exams accepted
BHU UET | KUK Entrance Exam | JMI Entrance ExamBachelor of Design in Animation (BDes)
Exams accepted
UCEED | NIFT Entrance Exam | NID Entrance ExamBA LLB (Bachelor of Arts + Bachelor of Laws)
Exams accepted
CLAT | AILET | LSAT IndiaBachelor of Journalism & Mass Communication (BJMC)
Exams accepted
LUACMAT | SRMHCAT | GD Goenka Test
What are the skill sets required for studying Pharmacy courses?