Gujarat Technological UniversityWinter 2024 examination

GTU 3140708 Discrete Mathematics (DM) Winter 2024 Question Paper & PDF

B.E. · Computer Engineering · Semester 4 · Subject code 3140708
Download official PDFView PDF here
Share with your class
Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 2:30 PM – 5:00 PM
Questions
5 with internal choice
No solutions on this paper yetNeed them for your exam? Ask once. Papers that students ask for are solved first, and we aim to add them within 24 hours.

17 of 25 questions are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 23 repeated 3140708 questions, most asked first

Q.1

14 Marks
(a)
3 marksSame type asked in 3 of 5 papers
Define onto function. Check whether the function 𝑓: ℝ → ℝ
defined by 𝑓(𝑥) = 𝑥² is one-one and onto.

Also asked in Summer 2026 Q3a, Winter 2023 Q1a

(b)
4 marksSame type asked in 3 of 5 papers
For the relation R = {(1,
1), (1,
2), (2,
1), (2,
2), (3,
3), (4,4)} on the set 𝐴 = {1,2,3,4}. Check whether it is reflexive, symmetric, anti-symmetric, transitive.

Also asked in Summer 2024 Q1b, Winter 2023 Q1b

(c)
7 marks
(
i)A history class contains 8 male students and 6 female students. Find the number 𝑛 of ways that the class can elect: (a) 1 class representative (b) 2 class representatives, 1 male and 1 female (c) 1 president and 1 vice president.
ii)Define elementary cycle, loop, tree and pendent vertex.3 Marks

Q.2

14 Marks
(a)
3 marks

Show that if every element in a group is its own inverse, then the group must be abelian.

(b)
4 marksSame type asked in 4 of 5 papers
Identify the statement (𝑝 → 𝑞) ⇆ (¬𝑝⋁𝑞) is tautology or
contradiction.

Also asked in Winter 2025 Q3a, Winter 2025 Q3b, Summer 2024 Q2a, Winter 2023 Q2a

(c)
7 marksSame type asked in 3 of 5 papers
Use a truth table to determine whether the following argument form
is valid.
𝑝 → 𝑞
𝑞 → 𝑟
∴ 𝑝 → 𝑟

Also asked in Summer 2024 Q2c OR, Winter 2023 Q2c

(c)
3 marksSame type asked in 3 of 5 papers
(
i)Symbolize the following expressions “𝑥 is the father of the mother of 𝑦” where 𝑃(𝑥): 𝑥 is a person. 𝐹(𝑥, 𝑦): 𝑥 is the father of 𝑦. 𝑀(𝑥, 𝑦): 𝑥 is the mother of 𝑦.
ii)Show that the premises “Everyone in this discrete mathematics class has taken a course in computer science” and “Marla is a student in this class” imply the conclusion “Marla has taken a course in computer science.”3 Marks

Also asked in Summer 2024 Q2c, Winter 2023 Q2c OR

Q.3

14 Marks
(a)
3 marksSame type asked in 2 of 5 papers
Define homomorphism. Let 𝐺 be the group of real numbers under
addition, and let 𝐺′ be the group of positive real numbers under
multiplication. Check whether the mapping 𝑓 ∶ 𝐺 → 𝐺′ defined by
𝑓(𝑎) = 2𝑎 is a homomorphism.

Also asked in Winter 2023 Q3a OR

(b)
4 marksSame type asked in 2 of 5 papers

Suppose that 100 mathematics students at a college taking at least one of the languages French, German, and Russian, given the following data: 65 study French, 45 study German, 42 study Russian, 20 study French and German, 25 study French and Russian, 15 study German and Russian.

1)Find the number of students who study all the three languages.
2)Find the number of students who study only French.

Also asked in Winter 2023 Q3b OR

(c)
7 marks
(
i)The subset 𝐻 = {0, 2} is a subgroup of (ℤ4, +4). Is 𝐻 a normal subgroup?
ii)Let ℤ𝑚 denotes the integers modulo 𝑚. Check whether ℤ𝑚 is a group under addition. If so, is it abelian group?3 Marks
(a)
3 marks
Find all the generators of cyclic group (ℤ5, +5).
(b)
4 marks
Prove that 𝐴 ∩ 𝐵̅ = 𝐴 ∩ 𝐶̅ if and only if 𝐴 ∩ 𝐵 = 𝐴 ∩ 𝐶.
(c)
7 marksSame type asked in 2 of 5 papers

Consider the ring ℤ30 = {0, 1, 2, … ,29} of integers modulo 30.

aFind −8 and −17.
bFind 11⁻¹, 13⁻¹ and 14−1.
cLet 𝑓 (𝑥) = 2 𝑥 + 4. Find the roots of 𝑓(𝑥) over ℤ30.

Also asked in Winter 2023 Q3c OR

Q.4

14 Marks
(a)
3 marksSame type asked in 2 of 5 papers

Let 𝐴 = {1, 2, 3, 4} and the relation 𝑅 = {(1,

1), (1,
4), (4,
1), (4,
4), (2,
2), (2,
3), (3,
2), (3,
3)} on 𝐴. Write the matrix of 𝑅 and check whether the relation is an equivalence.

Also asked in Winter 2023 Q4a OR

(b)
4 marks

Let 𝑋 = {2, 3, 6, 12, 24, 36} and the relation ≤ be such that 𝑥 ≤ 𝑦 if 𝑥 divides 𝑦. Find

i)Lower bound of {3,6},
ii)Upper bound of {3,6},
iii)GLB of {3,6}, if exist,
iv)LUB of {3,6}, if exist.
(c)
7 marksSame type asked in 2 of 5 papers

Solve the recurrence relation using the method of generating function 𝑎𝑛 − 5 𝑎𝑛−1 + 6𝑎𝑛−2 = 3𝑛, 𝑛 ≥ 2, 𝑎0 = 0, 𝑎1 = 2.

Also asked in Summer 2026 Q2c OR

(a)
3 marks
Let the relation 𝑅 = {(1,
2), (2,
3), (3,
3)} on 𝐴 = {1, 2, 3}. Find the transitive closure of 𝑅.
(b)
4 marksSame type asked in 4 of 5 papers
Solve 𝑎𝑛 = 2 𝑎𝑛−1 + 3𝑎𝑛−2, 𝑎0 = 1, 𝑎1 = 2.

Also asked in Winter 2025 Q3c OR, Summer 2024 Q4b OR, Winter 2023 Q4c OR

(c)
7 marksSame type asked in 4 of 5 papers

Draw Hasse diagram of 〈𝑆30, 𝐷〉. Prove that 〈𝑆30, 𝐷〉 is a lattice, where 𝐷 is the relation of “division” in ℕ such that for any 𝑎, 𝑏 ∈ ℕ, 𝑎𝐷𝑏 if and only if 𝑎 divides 𝑏 and 𝑆𝑛, (𝑛 ∈ ℕ) is the set of all divisors of 𝑛.

Also asked in Summer 2026 Q2c, Winter 2025 Q3c, Winter 2025 Q4a OR, Summer 2024 Q4b

Q.5

14 Marks
(a)
3 marks
Find the number of edges in a 𝑟-regular graph with 𝑛 vertices.
(b)
4 marksSame type asked in 3 of 5 papers
Check whether the following graphs are isomorphic or not.

Also asked in Summer 2026 Q3c, Summer 2024 Q5b

(c)
7 marksSame type asked in 3 of 5 papers

In which order does a pre-order, in-order and post-order traversal visit the vertices of the ordered rooted tree shown in figure?

GTU Discrete Mathematics (3140708) Winter 2024 Question 5(c) Diagram

Also asked in Summer 2026 Q5c OR, Winter 2023 Q5c OR

(a)
3 marksSame type asked in 2 of 5 papers

A tree 𝑇 has 4 vertices of degree 2, 3 vertices of degree 3, 1 vertex of degree 4. Find the number of pendant vertices in the tree 𝑇.

Also asked in Winter 2023 Q5a

(b)
4 marksSame type asked in 2 of 5 papers
Find reachable set of each node of the given digraph.

Also asked in Winter 2023 Q5b

(c)
7 marksSame type asked in 4 of 5 papers

Define adjacency matrix. Use Warshall's algorithm to obtain path matrix from the adjacency matrix of

Also asked in Summer 2026 Q3c OR, Summer 2024 Q5c, Winter 2023 Q5b OR

More Discrete Mathematics papers

Questions repeat across sessions. Working through two or three papers shows you which topics GTU asks most.

Summer 202670 marks · 5 questions · Solved
Winter 202570 marks · 5 questions
Summer 202470 marks · 5 questions
Winter 202370 marks · 5 questions

Other Semester 4 subjects

BE Computer

2140706
Numerical and Statistical Methods for Computer Engineering
2140707
Computer Organization
3140702
Operating System
3140705
Object Oriented Programming -I

Preparing with friends?

Send this paper to your class group. Every question has its own link.

About this paper

Official Gujarat Technological University (GTU) examination paper for Discrete Mathematics (DM) (Winter 2024, B.E. · Computer Engineering, Sem 4). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

Download official PDF All Discrete Mathematics Papers (5) →Report a typo or correction
ViewDownload PDF