DSTL PYQ 2021-22 AKTU Question Paper

AKTU · BTECH · Semester 3 · Discrete Structures & Theory of Logic · Session 2021-22 · PYQ

AKTU Discrete Structures & Theory of Logic previous year question paper 2021-22 for B.Tech Semester 3. Covers Set Theory, Relations, POSET & Lattices…

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Discrete Structures & Theory of Logic AKTU syllabus

  1. Unit 1: Set Theory, Relations, POSET & Lattices
  2. Unit 2: Functions & Boolean Algebra
  3. Unit 3: Theory of Logic
  4. Unit 4: Algebraic Structures (Group Theory)
  5. Unit 5: Graphs & Combinatorics

Questions in Discrete Structures & Theory of Logic AKTU PYQ 2021-22

  1. Q1a. Let A = {1,2,3,4,5,6} be the set and R = {(1,1) (1,5) (2,2) (2,3) (2,6) (3,2) (3,3,) (3,6) (4,4) (5,1) (5,5) (6,2) (6,3) (6,6)} be the relation defined on set A. Find Equivalence classes induced by R. (2 marks, 2021-22)
  2. Q1b. Solve Ackerman Function A (2,1). (2 marks, 2021-22)
  3. Q1c. State and justify “Every cyclic group is an abelian group”. (2 marks, 2021-22)
  4. Q1d. State Ring and Field with example. (2 marks, 2021-22)
  5. Q1e. Differentiate complemented lattice and distributed lattice. (2 marks, 2021-22)
  6. Q1f. State De Morgan’s law and Absorption Law. (2 marks, 2021-22)
  7. Q1g. Translate the conditional statement “If it rains, then I will stay at home” into contrapositive, converse and inverse statement. (2 marks, 2021-22)
  8. Q1h. State Universal Modus Ponens and Universal Modus Tollens laws. (2 marks, 2021-22)
  9. Q1i. Explain Euler’s formula. Determine number of regions if a planar graph has 30 vertices of degree 3 each. (2 marks, 2021-22)
  10. Q1j. Explain pigeonhole principle with example. (2 marks, 2021-22)
  11. Q2a. Justify that for any sets A, B, and C: i) (A – (A ∩ B)) = A – B ii) (A – (B ∩ C)) = (A – B) ᴜ (A – C) (10 marks, 2021-22)
  12. Q2b. Explain Cyclic group. Let H be a subgroup of a finite group G. Justify the statement “the order of H is a divisor of the order of G”. (10 marks, 2021-22)
  13. Q2c. Solve E(x,y,z,t) = ∑ (0,2,6,8,10,12,14,15) using K-map. (10 marks, 2021-22)
  14. Q2d. Construct the truth table for the following statements: i) (P→Q’)→P’ ii) P↔(P’˅Q’). (10 marks, 2021-22)
  15. Q2e. Solve the recurrence relation using generating function. an+2- 5an+1 +6an =2, with a0=3 and a1=7. (10 marks, 2021-22)
  16. Q3a. State Principle of Duality. Let A denote the set of real numbers and a relation R is defined on A such that (a,b)R(c,d) if and only if a^2 + b^2 = c^2 + d^2. Justify that R is an equivalence relation. (10 marks, 2021-22)
  17. Q3b. i) Let R = {(1,2) (2,3) (3,1)} defined on A = {1,2,3}. Find the transitive closure of R using Warshall’s algorithm. ii) Justify that “If f: A→B and g: B→C be one-to-one onto functions, then gof is also one to one onto and (gof)^-1= f^-1o g^-1”. (10 marks, 2021-22)
  18. Q4a. Define the binary operation * on Z by x*y=x + y + 1 for all x,y belongs to set of integers. Verify that (Z,*) is abelian group? Discuss the properties of abelian group. (10 marks, 2021-22)
  19. Q4b. i) Justify that “The intersection of any two subgroup of a group (G,*) is again a subgroup of (G,*)”. ii) Justify that “If a,b are the arbitrary elements of a group G then (ab)^2 = a^2b^2 if and only if G is abelian. (10 marks, 2021-22)
  20. Q5a. Define Modular Lattice. Justify that if ‘a’ and ‘b’ are the elements in a bounded distributive lattice and if ‘a’ has complement a′. then I) a ˅ (a′˄ b)=a˅ b II ) a˄ (a′˅ b)=a˄ b (10 marks, 2021-22)
  21. Q5b. i) Justify that (D36, \) 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. (10 marks, 2021-22)
  22. Q6a. Use rules of inference to Justify that the three hypotheses (i) “If it does not rain or if it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on.” (ii) “If the sailing race is held, then the trophy will be awarded.” (iii) “The trophy was not awarded.”… (10 marks, 2021-22)
  23. Q6b. Justify that the following premises are inconsistent. (i) If Nirmala misses many classes through illness then he fails high school. (ii) If Nirmala fails high school, then he is uneducated. (iii) If Nirmala reads a lot of books then he is not uneducated. (iv) Nirmala misses many classes through… (10 marks, 2021-22)
  24. Q7a. Explain the following terms with example: i. Graph coloring and chromatic number. ii. How many edges in K7 and K3,3 iii. Isomorphic Graph and Hamiltonian graph. iv. Bipartite graph. v. Handshaking theorem. (10 marks, 2021-22)
  25. Q7b. i. Justify that “In a undirected graph the total number of odd degree vertices is even”. ii. Justify that “The maximum number of edges in a simple graph is n(n-1)/2”. (10 marks, 2021-22)

AKTU paper codes: BCS303, KCS303, BCS303H, KCS303H

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