B.TechSemester 32023-24Discrete Structures Theory Of LogicBCS303
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Discrete Structures Theory Of Logic (BCS303) - AKTU Question Paper 2023-24

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 2023-24. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:B.Tech
Semester:Semester 3
Session:2023-24
University:AKTU / UPTU

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Questions Asked in 2023-24

Discrete Structures Theory Of Logic (BCS303) — complete question paper · 70 marks · 3 Hours

Section AAttempt all q u e s t i o n s i n b r i e f . 2 x 7 = 14
  • a
    Determine the greatest lower bound and least upper bound of th e set {2, 3, 6}, if they exist, in the Poset (D24, /)
  • b
    Express power set of each of these sets
  • c
    Investigate whether the function f(x) = x2 -1 is injective or not for
  • d
    Express E(x, y, z) = xy+ yꞌz int o its complete sum-of-products form. 2 2
  • e
    Construct inverse of the fo llowing statement “If I wake up early in the morning, then I will be healthy.”
  • f
    Show that identity element is unique in a group. 2 4
  • g
    Compare Euler circuit and H amiltonian circuit. 2 5
Section BAttempt any three o f t h e f o l l o w i n g : 7 x 3 = 21
  • a
    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
  • b
    Solve the following Bool ean functions using K-map
  • c
    Show the validity of t he following argument: hypotheses: “It is not sunny this afternoon and it is colder th an m yesterday. We will go swimming only if it is sunny. If we do no t go swimming, then we will take a canoe trip. If we take a canoe tr ip, then we will be home by sunset. conclusion: “We will be home b y sunset.”
  • d
    Let G= {1, -1, i, - i} with the binary operation multiplication be an algebraic structure, where i = √-1 then determine whether G is an Abelian group. Also if G is cyclic Group, then determine the generator of G
  • e
    Explain Pigeon hole principle. Describe generalized form of Pigeon hole principle. If 6 colors are to paint 37 homes. Show that at least 7 of them will be of same color
Section CAttempt any one p a r t o f t h e f o l l o w i n g : 7 x 1 = 7
  • a
    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 numb er of 0’s}. Show that whether R is reflexive, symmetric, transitive or a partial order relation
  • b
    Show that (D42, /) is lattice. Compare the distributive and complemented lattice with example
  • a
    Solve the following Boolean function using K-map: F(A,B,C) = (1,2,5,7) and D(0,4,6) using SOP
  • b
    If f: R R, g : RR and h: RR defined by f(x) = 3x2+2, g(x) =7x-5 and h(x) = 1/x. Compute the following composition functions. (i) (fogoh)(x) (ii) (gog)(x) (iii) (goh)(x)
  • a
    Test the validity of t he following argument. “If there was a ball game, then traveling was difficult. If they arrived on time, then traveling was not dif ficult. They arrived on time. T herefore, There was no ball game.”
  • b
    Describe  and  Quantifiers with example. “There is someone who got an A in the course” convert this sentence into predicate logic using quantifiers. Prove the following argument. All man are mortal. Socrates is a man. Therefore, Socrates is mortal
  • a
    Describe Algebraic structure, semigroup, monoid and group. A lso explain the relationship among them
  • b
    Consider group G = {1, 2, 3, 4, 5, 6} unde r multiplication modulo 7
  • a
    Construct the multiplication table of G
  • b
    Compute 2−1, 3−1, 6−1
  • c
    Compute the orders and subgroups generated by 2 and 3
  • a
    Compare bipartite and complete graph with example. Draw K 3,4 and K5. Explain why these two graphs are not planar
  • b
    Show that K 3,3 satisfies in equality |E| ≤ 3 |V| – 6, but it is non- planar.(V=No. of Vertices, E=No. of Edges, R=No. of Regions)

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)

2x

Solve the following Bool ean functions using K-map

Appeared in: 2023-24 · 2024-25

2x

Show the validity of t he following argument: hypotheses: “It is not sunny this afternoon and it is colder th an m yesterday. We will go swimming only if it is sunny. If we do no t go swimming, then we will take a canoe trip. If we take a canoe tr ip, then we will be home by sunset. conclusion: “We will be home b y sunset.”

Appeared in: 2023-24 · 2024-25

2x

Solve the following Boolean 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

Discrete Structures Theory Of Logic — Other Year Papers

AKTU Discrete Structures Theory Of Logic PYQs from other sessions

Discrete Structures Theory Of Logic2021-22Discrete Structures Theory Of Logic2022-23Discrete Structures Theory Of Logic2024-25Discrete Structures Theory Of Logic2025-26

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Syllabus & More PYQs

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📘 Discrete Structures & Theory of Logic — Unit-wise SyllabusBCS303AKTU 2nd Year SyllabusAKTU 2nd Year PYQs — All BranchesCSE 2nd Year SyllabusELECTRONICS COMPUTER ENGG 2nd Year Syllabus