Gujarat Technological UniversityWinter 2025 examination

GTU 3140708 Discrete Mathematics (DM) Winter 2025 Question Paper & PDF

B.E. · Computer Engineering · Semester 4 · Subject code 3140708
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 2:30 PM – 5:00 PM
Questions
5 with internal choice
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12 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 marks
Draw the graph with 4 nodes and 7 edges.
(b)
4 marks

Define simple graph, degree of a vertex, finite and infinite graphs and complete graph.

(c)
7 marks
(
i)If A = B = {1, 2, 3, 5, 6, 10, 15, 30} and relation R defined as a/b, where a∈A and b∈B. Find the relation matrix.
ii)Solve the recurrence relation an - 3an-1 = 2, n ≥ 1, a0 = 1.

Q.2

14 Marks
(a)
3 marks

Let A, B and C be the sets such that (A∩B∩C) = ∅, (A∩B) ≠ ∅, (A∩C) ≠ ∅, (B∩C) ≠ ∅. Draw the corresponding venn diagram.

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

Define subgroup of a group. Also, show that the subset H of a group of integers I is a subgroup under addition, where H = {...., -2m, -m, 0, m, 2m, .....}.

Also asked in Summer 2026 Q5b

(c)
7 marksSame type asked in 2 of 5 papers
How many integers between 1 to 2000 are divisible by 2, 3, 5 or 7.

Also asked in Summer 2026 Q1a

(c)
7 marks
Using venn diagram, prove the following
i)A∪(B∩C) = (A∪B)∩(A∪C)
ii)A⊕(B⊕C) = (A⊕B)⊕C

Q.3

14 Marks
(a)
3 marksSame type asked in 4 of 5 papers
Check whether the proposition ((pνq)Λ∼p)→q is contradiction, tautology or
contingency.

Also asked in Winter 2024 Q2b, Summer 2024 Q2a, Winter 2023 Q2a

(b)
4 marksSame type asked in 4 of 5 papers
Show that the proposition (p→(q→r))→((p→q)→(p→r)) is a tautology.

Also asked in Winter 2024 Q2b, Summer 2024 Q2a, Winter 2023 Q2a

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

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 18, 24} be ordered by the relation x divides y. Show that the relation is partial ordering and draw the Hasse diagram.

Also asked in Summer 2026 Q2c, Winter 2024 Q4c OR, Summer 2024 Q4b

(a)
3 marks
Show that the propositions p→q and ∼pvq are logically equivalent.
(b)
4 marks
Negate (opposite) each of the following statements
i)∀ x, |x| = x
ii)∃ x, x² = x
iii)If there is a riot, then someone killed.
iv)It is day light and all the people are arisen.
(c)
7 marksSame type asked in 4 of 5 papers
Solve the following recurrence relation
i)an - 7an-1 + 10an-2 = 0 given that a0 = 0, a1 = 3.
ii)an - 4an-1 + 4an-2 = 0 given that a0 = 1, a1 = 6.

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

Q.4

14 Marks
(a)
3 marks
Explain Partially order relation, Poset and Hasse diagram with example(s)
(b)
4 marks
Explain the regular graph and complete bipartite graph with example(s).
(c)
7 marks

Define tree and root. Also draw a tree with 10 vertices which has vertices either of degree 1 or of degree 3. Is it possible to draw a same type of tree with 11 vertices?

(a)
3 marksSame type asked in 4 of 5 papers

Let n be a positive integer, Sn be the set of all divisors of n. Let D denote the relation of division. Draw the lattices for

i)n = 24,
ii)n = 30

Also asked in Summer 2026 Q2c, Winter 2024 Q4c OR, Summer 2024 Q4b

(b)
12 marks
Draw the following grapghs
i)K3,4 Marks
ii)K4,4 Marks
iii)K5,4 Marks
iv)K5
(c)
7 marks
Find minimum spanning tree for the weighted graph given below

Q.5

14 Marks
(a)
3 marks
Define abelian group for any non empty set.
(b)
4 marksSame type asked in 2 of 5 papers

If G = {0, 1, 2, 3, 4, 5, 6, 7} and operation +8 is an addition modulo 8, then show that (G, +8) is an abelian group.

Also asked in Summer 2026 Q4b

(c)
7 marksSame type asked in 2 of 5 papers

Consider the set (C, +, . ), where C is the set of complex numbers and + and . are ordinary addition and multiplication operation. Show that (C, +, . ) is a field.

Also asked in Summer 2026 Q4c

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

Let Q+ be the set of all positive rational numbers and ∗ be a binary operation on Q+ defined by a∗b = ab/3 , then show that (Q+, ∗) is an abelian group.

Also asked in Summer 2026 Q4b

(b)
1 markSame type asked in 2 of 5 papers
Define cyclic group and show that the following groups are cyclic groups
i)Third roots of unity i.e. G = {1, ω, ω²}, ω3 =1 Mark
ii)G = {1, -1, i, -i}, where i² = -1

Also asked in Summer 2026 Q4b OR

(c)
7 marksSame type asked in 2 of 5 papers

Show that R = {a+b√2; a, b ∈ I} is an integral domain but not a field under the binary operations + (usual addition) and . (usual multiplication).

Also asked in Summer 2024 Q3c 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 202470 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

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About this paper

Official Gujarat Technological University (GTU) examination paper for Discrete Mathematics (DM) (Winter 2025, 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.

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