Set Theory

Paper Code: 
25GMAT201
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Investigates various operations that can be performed on sets, Such as union, Intersection, difference and complementation. These operations allow for combining, Comparing and analyzing sets.
  2. Explore the solution of problems from a mathematical perspective and prepare students to succeed in upper level math, Science, Engineering and other courses that require calculus. 
  3. Establishes a common language and toolkit for reasoning about mathematical structures and concepts. It is the foundation for many fields of study, Including logic, Algebra, Topology and analysis.

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

25GMAT201

 

 

 

 

 

 

 

Set Theory (Theory)

 

 

 

 

 

 

CO1: Discover the various set representations, Set operations etc..

CO2: Explain relations, ordered pairs, Cartesian products and related concepts.

CO3: Analyze different types of relations and their properties.

CO4: Explore functions, including ranges, Domains and codomains.

CO5: Analyze functions, sketch their graphs and perform operations on functions.

CO6: Contribute effectively in course-specific interaction.

 

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Assigned tasks

 

Quiz,

Individual and group tasks,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
Sets
12.00
 Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of a set of real numbers especially intervals (with notations), Universal set, Power set. Set operations (Union and Intersection of sets, Difference of sets, Complement of a set) with algebraic properties, Venn diagrams.
 
Unit II: 
Relations
12.00
 Ordered pairs, Cartesian product of sets, Definition of relation, Pictorial diagrams, Domain, Co-domain and range of a relation. 
 
Unit III: 
Types of relations
12.00

Reflexive, Symmetric, Anti-symmetric, Transitive and equivalence relations with examples. 

Unit IV: 
Functions
12.00
Function as a special type of relation. Pictorial representation of a function, Domain, Co-domain and range of a function, Real valued functions: Domain and range of these functions, Composite functions, Invertible functions.
 
Unit V: 
Type of functions
12.00
Constant, Identity, Polynomial, Rational, Modulus, Signum, Exponential, Logarithmic and greatest integer functions, with their graphs, Sum, Difference, Product and quotients of functions, One to one and onto functions.
 
References: 
  • David M. Burton, Elementary Number Theory, McGraw Hill, 2007.
  • J. P. Tremblyand R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw Hill Pub. Co. Ltd, New Delhi, 2010.
  • R.D. Sharma, “Mathematics for class 12 Part-2”, Dhanpat Rai and Co. New Delhi.
 
 

 

Academic Year: 
2025-2026
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