RTU Kota B.Tech AI 4th Semester Discrete Mathematical Structures Question Paper 2025

RTU Artificial Intelligence Discrete Mathematical Structures 2025 Paper Review

Preparing for the Rajasthan Technical University B.Tech Discrete Mathematical Structures exam requires absolute precision in logical reasoning and mathematical proofs. For Artificial Intelligence students, discrete mathematics is the primary language used to define state spaces, build knowledge representation systems, and formulate constraint satisfaction problems. You cannot design an expert system or a logical reasoning agent without a strict understanding of propositional logic and algebraic structures. The 2025 paper tests your ability to validate arguments, solve recurrence relations, and model networks using graph theory. Reviewing this specific branch paper shows you exactly how examiners structure the questions and allocate marks across the theoretical modules. This systematic preparation helps you approach your fourth-semester exam confidently.

Understanding the AI Branch Exam Pattern

The RTU theory examination is a three-hour paper worth 70 marks. The paper features three distinct sections designed to evaluate both basic definitions and complex theorem proofs.

• Part A: This section contains ten compulsory questions worth two marks each. You must write short definitions, evaluate simple truth values, or state specific principles like the Pigeonhole principle under 30 words.
• Part B: You will find seven questions here. You must answer five of them. Each question is worth four marks. Your answers require drawing Hasse diagrams, proving logical equivalences using truth tables, or solving basic permutations and combinations.
• Part C: This section offers five major questions. You need to answer three. Each question carries ten marks. These require detailed step-by-step proofs by mathematical induction, solving linear recurrence relations using generating functions, or executing complex graph isomorphism tests.

Core Topics Evaluated in the AI Paper

The 2025 question paper covers several critical modules that establish the mathematical baseline for advanced AI algorithms. Focus your study time on these specific areas to maximize your score.

Propositional and Predicate Logic

This module forms the foundation of AI inference engines. You must understand how to construct truth tables for compound propositions involving conjunctions, disjunctions, implications, and biconditionals. Examiners heavily test your ability to prove whether a logical statement is a tautology, a contradiction, or a contingency. Practice translating English sentences into logical expressions using universal and existential quantifiers. The paper frequently features ten-mark questions requiring you to validate a logical argument using the formal rules of inference without using a truth table.

Set Theory, Relations, and Functions

You need to master the operations on sets and the mathematical properties of relations. Study reflexive, symmetric, transitive, and antisymmetric relations thoroughly. You must know how to prove that a specific relation is an equivalence relation and calculate its equivalence classes. Another major focus area is Partial Order Relations (Posets). You must practice drawing clean Hasse diagrams and identifying the least upper bound and greatest lower bound for given elements. For functions, understand the conditions for injective (one-to-one), surjective (onto), and bijective mappings.

Graph Theory and Trees

Graphs represent the physical networks and decision spaces in AI algorithms. You must know the definitions and properties of bipartite graphs, complete graphs, and planar graphs. Practice calculating the chromatic number of a graph. Examiners evaluate your understanding of Eulerian circuits and Hamiltonian paths. For trees, study the properties of binary trees and spanning trees. Expect questions asking you to apply Euler’s formula for planar graphs to determine the number of edges, vertices, or regions.

Combinatorics and Recurrence Relations

This module tests your counting strategies and sequence analysis. You must practice the sum rule, product rule, and the principle of inclusion-exclusion. The 2025 paper places significant weight on solving linear recurrence relations. You must know how to find the homogeneous and particular solutions for second-order recurrence relations. Master the technique of solving these sequences using the method of generating functions, as this frequently appears as a mandatory ten-mark question in Part C.

Algebraic Structures

You must understand the hierarchy of mathematical systems. Study the definitions and axioms required to form a semi-group, monoid, group, and abelian group. Practice proving that a given set of numbers under a specific binary operation (like addition modulo n) forms a group. Understand the concepts of subgroups, cyclic groups, and Lagrange's theorem.

Answer Writing Strategy for High Marks

RTU evaluators look for clean logical steps, explicitly stated axioms, and well-drawn structural diagrams in your answer booklet. Use a blue pen for your general text explanations and mathematical steps, and use a black pen and ruler for drawing truth tables, Hasse diagrams, and graph structures.

In Part A, answer concisely. If a question asks for the definition of a chromatic number, define it directly as the minimum number of colors needed to color the vertices of a graph such that no two adjacent vertices share the same color.

In Part B, structure your proofs clearly. When using a truth table to prove logical equivalence, label the columns for every intermediate compound proposition. State the final conclusion explicitly at the bottom of the table, confirming that the columns match.

In Part C, continuous documentation of your logic is critical. When solving a ten-mark recurrence relation, clearly separate the steps for finding the characteristic equation, identifying the roots, writing the homogeneous solution, and calculating the particular constants using the initial conditions. When performing proofs by mathematical induction, explicitly label the Base Step, Inductive Hypothesis, and Inductive Step. Draw a clean box around your final mathematical formulas or derived solutions.

Time Management During the Exam

Allocate 20 minutes to Part A. Spend 40 minutes on Part B. Reserve the remaining 120 minutes for the three long-answer questions in Part C. Deriving rules of inference, writing out multi-variable truth tables, and solving recurrence relations require steady focus and significant time to prevent minor sign errors. This plan guarantees you 40 minutes per major question, giving you time to double-check your arithmetic and verify your logical derivations. Use the final 10 minutes to verify your question numbering, ensure your graph edges connect to the correct vertices clearly, and check that you have not skipped any intermediate steps in your proofs.