B.TechSemester 32022-23Discrete Structures Theory Of LogicKCS-303

Discrete Structures Theory Of Logic (KCS-303) - AKTU Question Paper 2022-23

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 2022-23. 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:2022-23

University:AKTU / UPTU

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Questions Asked in 2022-23

Discrete Structures Theory Of Logic (KCS-303) — complete question paper

Section AAttempt all questions in brief. 2 x 10 = 20

a
Identify whether ⎾x+y⏋=⎾x⏋+⎾y⏋, ⩝x,y ∈R, where ⎾x⏋is a ceiling function
b
Find the Maximal elements and m inimal elements form the following Hasse’s diagram
c
Define what is Big-O notation with respect of growth of functi ons
d
Find the composite mapping gof if f: RR is given by f(x) = ex and g: RR is given by g(x) = sinx
e
Draw an adjacency matrix for the following graph
f
Let A = { Φ, b}, then calculate A  P(A), where P(A) is a power set of A

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
S3 = {a,b,c,e},    S4 = {a,b,c} ,    S5 = {a,b} ,    S6 = {a,c} ,    S7 = {a}

h
Describe Planar graph and expres s Euler’s formula for planar graph. (i) Define normal subgroup. (j) Identify whether (p Λ q) → (p V q) is tautology or contradiction with using Truth table

Section BAttempt any three of the following: 10x3=30

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), (4,3) }

b
Let a function is defined as f: R-{3}→ R-{1}, f(x) = (x-1)/(x-3) , then show that f is a bijective function and also compute the inverse of f. Where R is a set of real numbers
c
(i) Express Converse, Inverse and Contrapositive of the following statement “If x+5=8 then x=3” (ii) Show that the statements P↔Q and (P ⋀ Q) V(⏋P ⋀ ⏋Q) are equivalent
d
Express the following (i) Euler graph and Hamiltonian graph (ii) Chromatic number of a graph (iii) Walk and path (iv) Bipartite graph
e
Solve the following recurrence relation by using generating function . an + 5an-1 + 6an-2= 42. 4n , where a0 = 1 and a1 = -2

Section CAttempt any one part of the following: 10x1=10

a
Let G = {1,-1,𝑖 ,െ 𝑖} with the operation of ordinary multiplication on G be an algebraic structure, where 𝑖=√-1. (i) Determine whether G is abelian. (ii) Determine the order of each element in G. (iii) Determine whether G is a cyclic group, if G is a cyclic group, then determine the generator/generators of the group G. (iv) Determine a subgroup of the group G
b
Let (G,*) and G’,* ’) be any two groups and let e and e’ be their respective identities. If f is a homomorphism of G into G’, then prove that
a
Use generating function to find the number of ways Rs 23 can b y paid by using 4 coins of Rs 5, 6 coins of Rs 2 and 4 coins of Rs 1
b
Using Pigeonhole principle find the minimum number n of integers to be selected from S={1,2,3,4,5,6,7,8,9} so that (i) the sum of two of the integers is even (ii) the difference of two of the n integers is 5
a
D e f i n e c o m p l e m e n t e d l a t t i c e a n d t h e n s h o w t h a t i n a d i s t r i b u t ive lattice, if an element has a complement then this complement is unique
b
Solve the following Boolea n functions using K-map
a
Prove the validity of the following argument. If Mary runs for office, She will be elected. If Mary attends t he meeting, she will run for office. Either Mary will attend the meeting or she will go to India. But Mary cannot go to India. “Thus Mary will be elected”
b
Convert the following two statements in quantified expressions of predicate logic (i) For every number there is a number greater than that number. (ii) Sum of every two integer is an integer. (iii) Not Every man is perfect. (iv) There is no student in the class who knows Spanish and German
a
Prove that the set of residues F={0,1,2,3,4} modulo 5 is a fie ld w.r.t. addition and multiplication of residue classes modulo 5. i.e. (F, +5, X5) is a field
b
Define Boolean algebra. Show t h a t a’.[(b’+c)’+ b.c] + [(a+b’)’.c] = a’.b using rules of Boolean Algebra. Where a’ is the complement of an element a

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 — KCS-303

Questions that appeared in more than one session, found by comparing 2 years of Discrete Structures Theory Of Logic papers (2021-22, 2022-23)

Solve the following recurrence relation by using generating function . an + 5an-1 + 6an-2= 42. 4n , where a0 = 1 and a1 = -2

Appeared in: 2021-22 · 2022-23

Discrete Structures Theory Of Logic — Other Year Papers

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Syllabus & More PYQs

Paper solve karne se pehle unit-wise syllabus dekh lo

📘 Discrete Structures & Theory of Logic — Unit-wise SyllabusBCS303 AKTU 2nd Year Syllabus AKTU 2nd Year PYQs — All Branches CSE 2nd Year Syllabus ELECTRONICS COMPUTER ENGG 2nd Year Syllabus