Discrete Structures Theory Of Logic (BCS303) - AKTU Question Paper 2024-25
B.Tech · Semester 3 · Free PDF Download
This is the official AKTU Discrete Structures Theory Of Logic Previous Year Question Paper for B.Tech Semester 3, academic session 2024-25. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.
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Questions Asked in 2024-25
Discrete Structures Theory Of Logic (BCS303) — complete question paper · 70 marks · 3 Hours
- 1Ůʲ Ő Ő 2 x 07 = 14 Q no. Question CO Leve
- aLet 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
- bLet A = {1,2,3} and B = {a, b} Compute the total number of possible relations from A to B
- cIf P(x) represents "x is a prime number" and Q(x) represents " x is odd," write the following statements in predicate logic: (a) "There exists an even prime number." (b) "All prime numbers greater than 2 are odd."
- dCalculate the composite mapping gof if f: R → R is given by f(x) = ex and g: R → R is given by g(x) = sin x
- eDefine Abelian group
- fSolve in how many ways can you a rrange the letters in the word "DISCRETE"?
- gIllustrate the following graph using an adjacency matrix: A graph with vertices V = {A, B, C, D} and edges E = {(A, B), (B, C), (C, D), (D
- 2ɻİ Ő Ů Ő: 07 x 3 = 21
- aExamine R = {(a, b) | a b (mod m)} is an equivalence relation on Z. Also ensure that if x1 y1 and x2 y2 then (x1 + x2) (y1 + y2)
- bSolve the following Bool ean function using K-map: F(A, B, C) = (1, 2, 5, 7) and D(0, 4, 6) using SOP
- cAnalyse the argument's validity: Premises: If a person is happy, they smile. John is smiling. Conclusion: John is happy
- dIn the group Z12 under addition modulo 12, consider the subgroup H = {0, 4, 8}. Compute all the distinct Cosets of H
- eExamine whether the graphs K3 and a graph formed by adding a single vertex in the middle of one edge of K3 are homeomorphic or not
- 3ɻİ Ő Ů Ő: 07 x 1 = 07
- aLet R = {(1, 2), (2, 3), (3, 1)} defined on A = {1, 2, 3}. C alculate the transitive closure of R using Warshall’s algorithm
- bi) Justify that (D42, \) is lattice. ii) Let L1 be the lattice defined as D6 and L2 be the lattice (P(S), ≤), where P(S) be the power set defined on set S = {a, b}. Justify that the two lattices are isomorphic
- 4ɻİ Ő Ů Ő: 07 x 1 = 07
- aSolve the following Boolean functions using K-map
- bLet f(x) = 3x + 5 and g(x) = x2 - 2x + 1. Evaluate f(3) and Classify f(x) and g(x) as one-to-one, onto, or neither
- 5ɻİ Ő Ů Ő: 07 x 1 = 07
- aJustify that the following premises are inconsistent. (i) If Alex misses many classes through illness then he fails high school. (ii) If Alex fails high school, then he is uneducated. (iii) If Alex reads a lot of books then he is not uneducated. (iv) Alex misses many classes through illness and reads a lot of books
- bShow the validity of the following argument: Hypotheses: “It is not sunny this afternoon and it is colder than yesterday. We will go swimming only if it is sunny. If we do not go swimming, then we will take a canoe trip. If we take a canoe trip, then we will be home by sunset. Conclusion: “We will be home by sunset.”
- 6ɻİ Ő Ů Ő: 07 x 1 = 07
- aCalculate the number of gener ators of the cyclic group of order 8
- bDetermine whether the set H = {0, 1, 5} is a subgroup of Z6 under addition modulo 6
- 7ɻİ Ő Ů Ő: 07 x 1 = 07
- aExpress the following (i) Euler graph and Hamiltonian graph (ii) Chromatic number of a graph (iii) Walk and path (iv) Bipartite graph
- bProve that in any group of 13 people, at least two must have t h e i r birthdays in the same month
Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.
Repeated Questions — BCS303
Questions that appeared in more than one session, found by comparing 3 years of Discrete Structures Theory Of Logic papers (2023-24, 2024-25, 2025-26)
Solve the following Bool ean function using K-map: F(A, B, C) = (1, 2, 5, 7) and D(0, 4, 6) using SOP
Appeared in: 2023-24 · 2024-25
Solve the following Boolean functions using K-map
Appeared in: 2023-24 · 2024-25
Show the validity of the following argument: Hypotheses: “It is not sunny this afternoon and it is colder than yesterday. We will go swimming only if it is sunny. If we do not go swimming, then we will take a canoe trip. If we take a canoe trip, then we will be home by sunset. Conclusion: “We will be home by sunset.”
Appeared in: 2023-24 · 2024-25
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