Discrete Structures

• Chapter 1: Basic Discrete Structures. Notes and past questions on Basic Discrete Structures for TU BSc CSIT Discrete Structures.
• Chapter 2: Integers and Matrices. Notes and past questions on Integers and Matrices for TU BSc CSIT Discrete Structures.
• Chapter 3: Logic and Proof Methods. Notes and past questions on Logic and Proof Methods for TU BSc CSIT Discrete Structures.
• Chapter 4: Induction and Recursion. Notes and past questions on Induction and Recursion for TU BSc CSIT Discrete Structures.
• Chapter 5: Counting and Discrete Probability. Notes and past questions on Counting and Discrete Probability for TU BSc CSIT Discrete Structures.
• Chapter 6: Relations and Graphs. Notes and past questions on Relations and Graphs for TU BSc CSIT Discrete Structures.

• List any four rules of inference. Using direct and indirect proof show that, for any real number $x$, if $x^3 - 7x^2 + x - 7 = 0$, then $... (2081)
• What are the necessary and sufficient conditions for graphs to have Euler path only and Euler circuit? Let $R$ be a relation defined on s... (2081)
• Determine whether the function f(x) = x-1 from set of integers to the set of integers is injective, surjective or bijective. Write the ty... (2081)
• Find the GCD of 12 and 16 using Extended Euclidean Algorithm. [5] (2081)
• Using mathematical induction show that $5 + 2 + 5 + 8 + ... + (3n-1) = \frac{n(3n+1)}{2}$ [5] (2081)
• State sum rule and product rule. If 26 integers are chosen from the set of consecutive integers {1,2,3,...,50}, prove that there are sure... (2081)
• Discuss about meet and join operation between Boolean matrices. What are the values of 5 mod 75 and -5 mod 77? [5] (2081)
• Define chromatic number. How does Kruskal's algorithm find Minimum Spanning Tree? [5] (2081)
• Solve the recurrence relation $a_n = a_{n-1} + 2a_{n-2}$ with initial conditions $a_0 = 2$ and $a_1 = 7$. [5] (2081)
• What is network flow? Give an example of saturated edge, unsaturated edge, and slack. [5] (2081)
• When do we use permutation rather than combination? How many 5-digit numbers can be generated using the digits 0 to 9, if each number sta... (2081)
• Define subset and power set. How do you prove correctness of recursive algorithm using Induction? Illustrate with an example. [5] (2081)
• Explain strong induction in detail. What is recursively defined function? Use mathematical induction to prove $7^{n+2} + 8^{2n+1}$ is div... (2080)
• State pigeonhole principle. Solve the recurrence relation $a_n = 5a_{n-1} - 6a_{n-2}$, with initial conditions $a_1 = 1$ and $a_2 = 3$.[10] (2080)
• State max flow min cut theorem. Find the value of maximal flow in the graph below:[10] (2080)

Frequently asked questions

Based on the official syllabus.