DSTL PYQ 2020-21 AKTU Question Paper

AKTU · BTECH · Semester 3 · Discrete Structures & Theory of Logic · Session 2020-21 · PYQ

AKTU Discrete Structures & Theory of Logic previous year question paper 2020-21 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 2020-21

  1. Q1a. Check whether the function f(x) = x^2 - 1 is injective or not for f : R→R. (2 marks, 2020-21)
  2. Q1b. Let R be a relation on set A with cardinality n. Write down the number of reflexive and symmetric relation on set A. (2 marks, 2020-21)
  3. Q1c. Define group. (2 marks, 2020-21)
  4. Q1d. Define ring. (2 marks, 2020-21)
  5. Q1e. Let A = {1, 2, 3, 4, 6, 8, 9, 12, 18, 24} be ordered by the relation ‘a divides b’. Find the Hasse diagram. (2 marks, 2020-21)
  6. Q1f. If L be a lattice, then for every a and b in L prove that a ˄ b = a if and only if a ≤ b. (2 marks, 2020-21)
  7. Q1g. Write the negation of the following statement: “If I wake up early in the morning, then I will be healthy.” (2 marks, 2020-21)
  8. Q1h. Express the following statement in symbolic form: “All flowers are beautiful.” (2 marks, 2020-21)
  9. Q1i. Define complete and regular graph. (2 marks, 2020-21)
  10. Q1j. Prove that the maximum number of vertices in a binary tree of height h is 2^(h+1), h ≥ 0. (2 marks, 2020-21)
  11. Q2a. If f : R → R, g : R → R and h : R → R defined by f(x) = 3x^2 + 2, g(x) = 7x – 5 and h(x) = 1/x. Compute the following composition functions: i. (fogoh)(x), ii. (gog)(x), iii. (goh)(x), iv. (hogof)(x) (10 marks, 2020-21)
  12. Q2b. State and prove Lagrange theorem for group. (10 marks, 2020-21)
  13. Q2c. Prove that in any lattice the following distributive inequalities hold: i. a ˄ (b ˅ c) ≥ (a ˄ b) ˅ (a ˄ c), ii. a ˅ (b ˄ c) ≤ (a ˅ b) ˄ (a ˅ c) (10 marks, 2020-21)
  14. Q2d. Prove the validity of the following argument: “If I get the job and work hard, then I will get promoted. If I get promoted, then I will be happy. I will not be happy. Therefore, either I will not get the job, or I will not work hard.” (10 marks, 2020-21)
  15. Q2e. If a connected planar graph G has n vertices, e edges and r region, then n – e + r = 2. (10 marks, 2020-21)
  16. Q3a. Prove by mathematical induction for all positive integers that 3.5^(2n+1) + 2^(3n+1) is divisible by 17. (10 marks, 2020-21)
  17. Q3b. Find the numbers between the 100 to 1000 that are divisible by 3 or 5 or 7. (10 marks, 2020-21)
  18. Q4a. A subgroup H of a group G is a normal subgroup if and only if g^-1 hg ϵ H for every h ϵ H and g ϵ G. (10 marks, 2020-21)
  19. Q4b. In a group (G, *) prove that: i. (a^-1)^-1 = a, ii. (ab)^-1 = b^-1a^-1 (10 marks, 2020-21)
  20. Q5a. Simplify the Boolean function F (A, B, C, D) = ∑ (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11). Also draw the logic circuit of simplified F. (10 marks, 2020-21)
  21. Q5b. Simplify the following Boolean expressions using Boolean algebra: i. xy + x'z + yz, ii. C(B + C)(A + B + C), iii. A + B(A + B) + A(A' + B), iv. XY + (XZ)' + XY'Z(XY + Z) (10 marks, 2020-21)
  22. Q6a. Define tautology, contradiction and contingency? Check whether (p ˅ q) ˄ (~ p ˅ r) → (q ˅ r) is a tautology, contradiction or contingency. (10 marks, 2020-21)
  23. Q6b. Translate the following statements in symbolic form: i. The sum of two positive integers 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. (10 marks, 2020-21)
  24. Q7a. Construct the binary tree whose inorder and preorder traversal is given below. Also, find the postorder traversal of the tree. Inorder: d, g, b, e, i, h, j, a, c, f. Preorder: a, b, d, g, e, h, i, j, c, f (10 marks, 2020-21)
  25. Q7b. Solve the following recurrence relation: an – an–1 + 20an–2 = 0 where a0 = – 3, a1 = – 10 (10 marks, 2020-21)

AKTU paper codes: BCS303, KCS303, BCS303H, KCS303H

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