DSTL Unit 1 Notes AKTU (BCS303)

AKTU · BTECH · Semester 3 · Discrete Structures & Theory of Logic · Unit 1 · Notes

AKTU Discrete Structures & Theory of Logic (BCS303) Unit 1 notes for B.Tech Semester 3 – Set Theory, Relations, POSET & Lattices. Topics: Set Theory…

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Unit 1: Set Theory, Relations, POSET & Lattices – AKTU syllabus topics

  • Set Theory
  • Relations: Equivalence Relations, Closure of Relations
  • POSET & Hasse Diagram
  • Lattices

Most asked AKTU PYQ questions from Unit 1

  1. Q3b. Find the numbers between the 100 to 1000 that are divisible by 3 or 5 or 7. (10 marks, 2020-21)
  2. 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)
  3. 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)
  4. Q3b. i) 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. (7 marks, 2024-25)
  5. Q2a. Construct the Hasse Diagram for (P(S), ⊆) where P(S) is a power set defined on set S={a, b, c}. Determine whether it is a Lattice or not. (7 marks, 2023-24)
  6. Q3a. Let R be a binary relation on the set of all strings of 0 and 1 such that R = {(a,b): a and b have same number of 0’s}. Show that whether R is reflexive, symmetric, transitive or a partial order relation. (7 marks, 2023-24)
  7. Q3b. Show that (D42, /) is lattice. Compare the distributive and complemented lattice with example. (7 marks, 2023-24)
  8. Q1g. Draw the Hasse’s diagram of the POSET (L, ⊆) , where L = {S0, S1, S2, S3, S4, S5, S6, S7}, where the sets are given by S0 = {a,b,c,d,e,f}, S1 = {a,b,c,d,e} , S2 = {a,b,c,e,f}, S3 = {a,b,c,e}, S4 = {a,b,c} , S5 = {a,b} , S6 = {a,c} , S7 = {a} (2 marks, 2022-23)
  9. Q2a. Identify whether the each of the following relations defined on the set X = {1,2,3,4} are reflexive, symmetric, transitive and/or antisymmetric? (i) R1 = { (1,1), (1,2), (2,1) } (ii) R2 = { (1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1), (4,4) } (iii) R3 = { (2,1), (3,1), (3,2), (4,1), (4,2),… (10 marks, 2022-23)
  10. Q2e. Solve the following recurrence relation by using generating function. an + 5an-1 + 6an-2= 42. 4n , where a0 = 1 and a1 = -2 (10 marks, 2022-23)

AKTU paper codes: BCS303, KCS303, BCS303H, KCS303H

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