(SEM-III) THEORY EXAMINATION 2022-23 DISCRETE STRUCTURES & THEORY OF LOGIC

This question paper is designed to evaluate the student’s understanding of the fundamental concepts of Discrete Mathematics, including logic, set theory, relations, functions, combinatorics, graph theory, group theory, lattices, recurrence relations, Boolean algebra, generating functions, and predicate logic. The paper is divided into three sections – A, B, and C, covering both conceptual clarity and problem-solving ability.

Section A consists of short-answer questions intended to test the student’s basic knowledge of essential definitions, properties, and introductory concepts such as Big-O notation, ceiling functions, planar graphs, power sets, truth tables, normal subgroups, and composite mappings. These questions assess conceptual understanding and familiarity with core terms.

Section B contains descriptive and analytical questions requiring detailed explanations, proofs, and computations. This section evaluates the student’s ability to apply mathematical theories to solve problems involving relations and their properties, bijective functions, logical equivalence, Euler/Hamiltonian graphs, chromatic number, recurrence relations using generating functions, and other important concepts. Students are expected to demonstrate reasoning, step-by-step problem solving, and clarity in mathematical writing.

Section C focuses on advanced application-oriented and proof-based questions from group theory, generating functions, Boolean algebra, lattices, pigeonhole principle, logical arguments, and field properties. These questions test the student’s depth of understanding, ability to construct formal proofs, solve higher-level mathematical problems, and apply discrete mathematics concepts to abstract structures.

Overall, this question paper aims to measure the student's logical thinking, analytical skills, proof techniques, and mastery of discrete mathematical structures, which form the foundation for advanced topics in computer science and engineering.