(SEM III) THEORY EXAMINATION 2024-25 DISCRETE STRUCTURES & THEORY OF LOGIC

1. Overview of the Examination Structure

The BCS303 – Discrete Structures & Theory of Logic examination for B.Tech (Semester III) is a three-hour theory paper of seventy marks. The paper is divided into three sections, each designed to test different levels of understanding—from basic set theory and logic to Boolean algebra, relations, groups, and graph theory. The exam effectively combines conceptual questions, analytical reasoning, and problem-solving tasks in accordance with the foundational requirements of discrete mathematics.

2. Section A – Brief Conceptual Questions

Section A contains seven short questions of two marks each, targeting basic understanding of sets, relations, predicate logic, mappings, groups, combinatorics, and graph representation. The questions ask students to compute union and intersection of sets involving primes and odd numbers, determine the number of possible relations between two sets, and express logical statements using predicate logic notation. Students are further required to compute composite functions, define Abelian groups, and determine permutations of letters in the word “DISCRETE.” The final question involves constructing an adjacency matrix for a simple four-vertex graph. This section assesses clarity of fundamental concepts and the ability to perform small but precise computations.

3. Section B – Intermediate Analytical Reasoning

Section B requires students to attempt any three descriptive questions, each carrying seven marks. The questions explore deeper theoretical concepts such as proving that a modular relation forms an equivalence relation and showing that addition preserves equivalence classes. Another question demands solving a Boolean function using Karnaugh Maps with specified minterms and don't-care conditions. Logical reasoning is tested through the analysis of argument validity using rules of inference. Group theory concepts are examined by computing all distinct cosets of a given subgroup in Z₁₂. A graph-theoretic question asks students to determine whether two graphs are homeomorphic. This section evaluates analytical reasoning, mathematical proof skills, and the ability to apply abstract theoretical ideas.

4. Section C – Advanced Problem-Solving and Conceptual Mastery

Section C contains five question sets, each with two alternatives, from which one must be answered. The questions in this section emphasize advanced topics and problem-solving abilities. Students may compute the transitive closure of a relation using Warshall’s algorithm or prove isomorphism between lattices. Boolean algebra also appears again, with the requirement to simplify four-variable functions using K-maps. Another alternative tests understanding of functions by evaluating f(3) and classifying functions as one-to-one or onto.

Additional questions examine the consistency or inconsistency of logical premises involving daily-life scenarios, or validate an argument using formal inference. Group theory questions require computing generators of cyclic groups or determining whether a subset forms a subgroup under modulo addition. The final choice focuses on graph theory: describing Eulerian and Hamiltonian graphs, chromatic numbers, walks and paths, bipartite graphs, or proving a pigeonhole-principle-based result that among thirteen people, at least two share the same birth month. This section tests deep conceptual clarity, proof construction, and the ability to connect discrete structures to practical reasoning.

5. Purpose and Assessment Approach

Overall, the BCS303 exam is structured to thoroughly assess a student's grounding in discrete mathematics and logical reasoning. Section A verifies the fundamentals, Section B measures intermediate problem-solving and validation skills, and Section C evaluates higher-order understanding through algorithms, algebraic structures, argumentation, and graph theory. The structure ensures that students demonstrate not only knowledge but also the ability to analyze, prove, simplify, classify, and logically infer—skills foundational to computer science and engineering.