The uploaded file is a B.Tech (Semester III) Theory Examination – 2018–2019 question paper for the subject DISCRETE STRUCTURES AND THEORY OF LOGIC, with Sub Code RCS301.
It contains 2 printed pages, carries 70 marks, and the exam duration is 3 hours.
This exam paper evaluates the student's understanding of discrete mathematical structures, logic fundamentals, relations, algebraic structures, and problem-solving skills relevant to computer science.
PAGE 1 OVERVIEW
Page 1 contains the exam title, instructions, and SECTION-A.
SECTION A — Short Questions (2 × 7 = 14 Marks)
Students must answer all seven short questions. These questions focus on definitions, basic set operations, logic concepts, and diagrammatic understanding.
The topics include:
Power set of given sets such as {a}, {i}, {0}, {a, i} Definition of Ring and Field
Hasse Diagram for D₁₀ Symmetric difference
Permutation groups Conditional and bi-conditional statements
Transitive relations and proofs
This section tests fundamental conceptual clarity in sets, algebraic structures, and logic.
PAGE 2 OVERVIEW
Page 2 consists of SECTION C (as visible in the image), which contains long, reasoning-based mathematical problems.
SECTION C — Long, Analytical Problems (7 Marks Each)
Students must attempt any one part of each question number.
Below are the details visible on Page 2:
Question 3 — Proof & Relation-Based Problem
(a)
A number theory–based proof:
Prove:
If n is a positive integer, then 133 divides 11ⁿ⁺¹ + 12ⁿ⁻¹
This tests mathematical induction or modular arithmetic skills.
(b)
A relation defined on a set of strings:
Given a positive integer n, relation Rₙ is defined such that:
s Rₙ t iff
|s| ≥ n, |t| ≥ n,
First n characters of s and t match.
Students must determine the equivalence class of the string 0111 under this relation.
This checks understanding of:
Reflexive, symmetric, transitive relations
Equivalence classes
String operations
Question 4 — Algebraic Structure & Group Theory
Let G = {1, −1, i, −i} under multiplication, where i is the imaginary unit.
Tasks include:
Showing whether G is Abelian or not Determining if G forms a group under the given operation
This question focuses on: Algebraic structures
Group axioms Commutativity
Complex number multiplication tables
OVERALL SUMMARY
This exam paper is designed to test the student’s understanding of:
Set theory Logic statements and equivalence
Relations and equivalence classes Hasse diagrams & partial orderings
Algebraic structures: rings, fields, groups Number theory proofs
Permutations & symmetric groups
Mathematical reasoning and discrete structures essential for computer science
It blends theory, definitions, proofs, and diagram-based questions, making it ideal for both academic preparation and conceptual strengthening.
