(SEM III) THEORY EXAMINATION 2018-19 DISCRETE STRUCTURES AND THEORY OF LOGIC

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.