Discrete Structures & Theory of Logic (BCS303) AKTU previous year questions 2020–2026
Every Discrete Structures & Theory of Logic question from 7 AKTU papers, tagged by unit, topic and marks. A few recent questions from each unit are listed below; open the page to filter by unit, topic or mark type.
Unit 1: Set Theory, Relations, POSET & Lattices – AKTU PYQs
- Define Lattice and the properties of lattice. (7 marks, 2026, Lattices)
- If R is an equivalence relation on A, then prove that R-1 is also equivalence relation on A. (7 marks, 2026, Relations)
- Define a lattice and state the meaning of upper bound and lower bound in a lattice. (2 marks, 2026, Lattices)
- Explain the following terms: (i) POSET (ii) Hasse Diagram (7 marks, 2026, POSET & Hasse Diagram)
- Let A = {x: x is a prime number less than 20} and B = {x: x is an odd number less than 20} Compute A U B and A ∩ B. (2 marks, 2025, Set Theory)
Unit 2: Functions & Boolean Algebra – AKTU PYQs
- Use a Karnaugh map to find a minimal sum for E= y’t’ + y’z’t + x’y’zt + yzt’ (7 marks, 2026, Boolean Algebra)
- Show that the number of minimal Boolean function in n variables are 2’’. (7 marks, 2026, Boolean Algebra)
- Explain the basic concepts of Boolean algebra and state any four fundamental laws of Boolean algebra. (7 marks, 2026, Boolean Algebra)
- What is meant by a reflexive relation? State its basic property. (2 marks, 2026, Functions)
- Find the domain and range of the function f(x)=1-|x|. (2 marks, 2026, Functions)
Unit 3: Theory of Logic – AKTU PYQs
- Prove that the statement “if n is an integer, then n2-n+4! Is a prime number” is false. (7 marks, 2026, Theory of Inference)
- Explain the following terms with suitable example: (i) Converse (ii) Disjunction (iii) Conjunction (7 marks, 2026, Propositional Logic)
- Translate the following statements in symbolic form: (i) The sum of two positive integer is always positive. (ii) Everyone is loved by someone. (iii) Some people are not admired by everyone. (iv) If a person is female and is a parent, then this person is someone’s mother. (7 marks, 2026, Predicate Logic)
- What is meant by an existential quantifier? Explain it with a simple statement. (2 marks, 2026, Predicate Logic)
- Analyse the argument's validity: Premises: If a person is happy, they smile. John is smiling. Conclusion: John is happy. (7 marks, 2025, Theory of Inference)
Unit 4: Algebraic Structures (Group Theory) – AKTU PYQs
- Let H be a subgroup of a finite group G. Prove that order of H is a divisor of order G. (7 marks, 2026, Cosets & Lagrange's Theorem)
- How many generators are there of the cyclic group G of order 10. (7 marks, 2026, Groups & Subgroups)
- State and prove Lagrange’s theorem. (7 marks, 2026, Cosets & Lagrange's Theorem)
- Define zero divisor of a ring. (2 marks, 2026, Rings & Fields)
- Define Abelian group. (2 marks, 2025, Groups & Subgroups)
Unit 5: Graphs & Combinatorics – AKTU PYQs
- Let G be a 3-regualr graph with n vertices. What is the sum of the degree of the vertices? Show that in such a graph n must be even. (7 marks, 2026, Graphs & Terminology)
- Prove that if a connected graph G is decomposed into two subgraphs g1 and g2, there must be at least one vertex common between g1 and g2. (7 marks, 2026, Isomorphism & Homeomorphism)
- Show that in any room of people who have been doing handshaking there will always be at least two people who have shaken hands the same number of times. (7 marks, 2026, Combinatorics & Counting)
- How many 4 digits number can be formed by using the digits 2,4,6,8 when the repetition of digits is allowed. (2 marks, 2026, Combinatorics & Counting)
- Draw a graph that has a Hamiltonian path not have a Hamiltonian circuit. (2 marks, 2026, Euler & Hamiltonian Paths)