DSTL PYQ 2019-20 AKTU Question Paper

AKTU · BTECH · Semester 3 · Discrete Structures & Theory of Logic · Session 2019-20 · PYQ

AKTU Discrete Structures & Theory of Logic previous year question paper 2019-20 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 2019-20

  1. Q1a. Define various types of functions. (2 marks, 2019-20)
  2. Q1b. How many symmetric and reflexive relations are possible from a set A containing ‘n’ elements? (2 marks, 2019-20)
  3. Q1c. Let Z be the group of integers with binary operation * defined by a*b=a+b-2, for all a,b∈ Z . Find the identity element of the group (Z,*) (2 marks, 2019-20)
  4. Q1d. Show that every cyclic group is abelian. (2 marks, 2019-20)
  5. Q1e. Prove that a lattice with 5 elements is not a boolean algebra. (2 marks, 2019-20)
  6. Q1f. Write the contra positive of the implication: “if it is Sunday then it is a holiday”. (2 marks, 2019-20)
  7. Q1g. Show that the propositions p→qand ¬p∨q are logically equivalent. (2 marks, 2019-20)
  8. Q1h. Show that there does not exist a graph with 5 vertices with degrees 1, 3, 4, 2, 3 respectively. (2 marks, 2019-20)
  9. Q1i. Obtain the generating function for the sequence 4, 4, 4, 4, 4, 4 (2 marks, 2019-20)
  10. Q1j. Define Pigeon hole principle. (2 marks, 2019-20)
  11. Q2a. Prove that 1/√1 + 1/√2 + 1/√3 + ......... + 1/√n > √n for n≥2 using principle of mathematical induction (10 marks, 2019-20)
  12. Q2b. What do you mean by cosets of a subgroup? Consider the group Z of integers under addition and the subgroup H = {...., -12, -6, 0, 6 12, ......} considering of multiple of 6 (i) Find the cosets of H in Z (ii) What is the index of H in Z. (10 marks, 2019-20)
  13. Q2c. Show that the following are equivalent in a Boolean algebra a≤b ⇔ a*b'=0 ⇔ b'≤a' ⇔ a'⊕b=1 (10 marks, 2019-20)
  14. Q2d. Show that ((P∨Q)∧(¬Q∨¬R))∨(¬P∨¬Q)∨(¬P∨¬R) is a tautology by using equivalences. (10 marks, 2019-20)
  15. Q2e. Define planar graph. Prove that for any connected planar graph, v - e + r = 2 Where v, e, r is the number of vertices, edges, and regions of the graph respectively. (10 marks, 2019-20)
  16. Q3a. Find the numbers between 1 to 500 that are not divisible by any of the integers 2 or 3 or 5 or 7. (10 marks, 2019-20)
  17. Q3b. Is the “divides” relation on the set of positive integers transitive? What is the reflexive and symmetric closure of the relation? R = {(a, b) | a > b} on the set of positive integers? (10 marks, 2019-20)
  18. Q4a. What is Ring? Define elementary properties of Ring with example. (10 marks, 2019-20)
  19. Q4b. Prove or disprove that intersection of two normal subgroups of a group G is again a normal subgroup of G. (10 marks, 2019-20)
  20. Q5a. Let (L,∨,∧,≤) be a distributive lattice and a,b∈L. if a∧b=a∧c and a∨b=a∨c then show that b=c (10 marks, 2019-20)
  21. Q5b. Obtain the principle disjunctive and conjunctive normal forms of the formula (p→r)∧(q↔p) (10 marks, 2019-20)
  22. Q6a. Explain various Rules of Inference for Propositional Logic. (10 marks, 2019-20)
  23. Q6b. Prove the validity of the following argument “if the races are fixed so the casinos are crooked, then the tourist trade will decline. If the tourist trade decreases, then the police will be happy. The police is never happy. Therefore, the races are not fixed. (10 marks, 2019-20)
  24. Q7a. Solve the following recurrence equation using generating function G(K) -7 G(K-1) + 10 G(K-2) = 8K + 6 (10 marks, 2019-20)
  25. Q7b. A collection of 10 electric bulbs contain 3 defective ones (i) In how many ways can a sample of four bulbs be selected? (ii) In how many ways can a sample of 4 bulbs be selected which contain 2 good bulbs and 2 defective ones? (iii) In how many ways can a sample of 4 bulbs be selected so that… (10 marks, 2019-20)

AKTU paper codes: BCS303, KCS303, BCS303H, KCS303H

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