Engineering B.E. (Computer Engineering) Sem 3 Discrete Structures and Graph Theory Dec 2022 DSE Question Paper - Mumbai University | munotes
Get access to whole semester resourcesSemester Pass
MU B.E. (Computer Engineering) student group
Free to join
Loading PDF...
Older exam
None: this is the earliest we hold
Newer exam
Dec 2022
Semester-end · Discrete Structures and Graph Theory
→
Questions asked in this paper
Time: 3 Hours Marks: 80
N.B. : (1) Question Number 1 is compulsory
(2) Solve any three questions from the remaining questions
(3) Make suitable assumptions if needed
(4) Assume appropriate data whenever required. State all assumptions clearly
Q.1 Solve any four of the following questions
a) Prove using Mathematical Induction that 1+5+9+ ....... + (4n-3) = n (2n-1) 5
b) Find the relation set & relation matrix for the following digraph. Determine in degree
& out degree of each vertex. 5
c) State the pigeon hole principle. If 30 people are assembled in a room, then show that
of them must have their birthday on the same day of a week. 5
d) Explain the following terms with suitable example: 5
i) Eulerian graph
e) What is a partial order relation? Determine the hasse diagram for following relation 5
a) What is a transitive closure? Let A={al, a2, a3, a4, a5}. Find the transitive closure of
R using Warshall’s algorithm where relation matrix Me is given as follows- 10
b) What are the isomorphic graphs? Determine whether following graphs are
a) Among the integers 1 to 300, 8
i) How many of them are not divisible by 3 nor by 5 nor by 7?
il) How many of them are divisible only by 3?
b) There are 6 Communication Skills books, 8 Engg. Mathematics books, 10 books on C
Programming. How many ways can be used to choose 2 books of different categories
c) What is a partition set? Determine whether each of the following is a partition. Justify
Let X= {1,2,3,....8,9}. Determine whether or not each of following is a partition
a) What is a group? Let A={5, 10 ,15, 20} 10
i) Prepare the composition table w.r.t. the operation of multiplication modulo 25
ii) Whether it is an abelian group? Justify your answer
iii) Find the inverses of all the elements
iv) Whether it is a cyclic group?
b) What is a ring? Let A= {0, 1, 2, 3, 4, 5}. Determine whether a set A with addition
modulo 6 & multiplication modulo 6 is a commutative ring? Justify your answer. 10
a) Define a lattice. Prove that in a distributive lattice the complement of any element is
unique. Determine whether is a distributive lattice. Find the complements of all
b) Define the term bijective function. Let f: be a function defined by f(x) = 2x-3
Determine whether it is a bijective function. 6
Draw the graph G corresponding to each adjacency matrix
b) What is a planer graph? A connected planer graph has 8 vertices having degrees
2,2,2,3,3,3,4,4. How many edges are there in this graph? 6
c) Write the following statements in a symbolic form using quantifiers. Assume a
i) All students have taken a course in mathematics
il) There is a girl student in a class who is also a sports person
ili) Some students are intelligent, but not hardworking
N.B. : (1) Question Number 1 is compulsory
(2) Solve any three questions from the remaining questions
(3) Make suitable assumptions if needed
(4) Assume appropriate data whenever required. State all assumptions clearly
Q.1 Solve any four of the following questions
a) Prove using Mathematical Induction that 1+5+9+ ....... + (4n-3) = n (2n-1) 5
b) Find the relation set & relation matrix for the following digraph. Determine in degree
& out degree of each vertex. 5
c) State the pigeon hole principle. If 30 people are assembled in a room, then show that
of them must have their birthday on the same day of a week. 5
d) Explain the following terms with suitable example: 5
i) Eulerian graph
e) What is a partial order relation? Determine the hasse diagram for following relation 5
a) What is a transitive closure? Let A={al, a2, a3, a4, a5}. Find the transitive closure of
R using Warshall’s algorithm where relation matrix Me is given as follows- 10
b) What are the isomorphic graphs? Determine whether following graphs are
a) Among the integers 1 to 300, 8
i) How many of them are not divisible by 3 nor by 5 nor by 7?
il) How many of them are divisible only by 3?
b) There are 6 Communication Skills books, 8 Engg. Mathematics books, 10 books on C
Programming. How many ways can be used to choose 2 books of different categories
c) What is a partition set? Determine whether each of the following is a partition. Justify
Let X= {1,2,3,....8,9}. Determine whether or not each of following is a partition
a) What is a group? Let A={5, 10 ,15, 20} 10
i) Prepare the composition table w.r.t. the operation of multiplication modulo 25
ii) Whether it is an abelian group? Justify your answer
iii) Find the inverses of all the elements
iv) Whether it is a cyclic group?
b) What is a ring? Let A= {0, 1, 2, 3, 4, 5}. Determine whether a set A with addition
modulo 6 & multiplication modulo 6 is a commutative ring? Justify your answer. 10
a) Define a lattice. Prove that in a distributive lattice the complement of any element is
unique. Determine whether is a distributive lattice. Find the complements of all
b) Define the term bijective function. Let f: be a function defined by f(x) = 2x-3
Determine whether it is a bijective function. 6
Draw the graph G corresponding to each adjacency matrix
b) What is a planer graph? A connected planer graph has 8 vertices having degrees
2,2,2,3,3,3,4,4. How many edges are there in this graph? 6
c) Write the following statements in a symbolic form using quantifiers. Assume a
i) All students have taken a course in mathematics
il) There is a girl student in a class who is also a sports person
ili) Some students are intelligent, but not hardworking
Read from the scan above, so a character or two may differ. The scan is the original.
Something wrong on this page? Report it and we will check it against the scan.
Quick Help
No. The full paper opens straight away, with no login and nothing to pay.
Related Resources
Something wrong with this paper? Report it.
Connected Papers
Engineering / B.E. (Computer Engineering) · 250 papers
May 2026
May 2026
May 2026
May 2026
May 2026
Dec 2025
Dec 2025
Dec 2025
Dec 2025
Dec 2025
Dec 2025
May 2025
May 2025
May 2025
May 2025
May 2025
May 2025
May 2025
Dec 2024
Dec 2024
Dec 2024
Dec 2024
Dec 2024
Dec 2024
May 2024
May 2024
May 2024
May 2024
May 2024
Dec 2023
Dec 2023
Dec 2023
Dec 2023
Dec 2023
May 2023
May 2023
May 2023
May 2023
Dec 2022
Dec 2022
Dec 2022
Dec 2022
Dec 2022
Dec 2022
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer Set 2
May 2019
May 2019
May 2019
May 2019
May 2019
May 2019
May 2019 - CBSGS
May 2019 - CBSGS
May 2019 - R16
May 2019 - R16
May 2026
May 2026
May 2026
May 2026
May 2026
Dec 2025
Dec 2025
Dec 2025
Dec 2025
Dec 2025
Dec 2025
Dec 2025
May 2025
May 2025
May 2025
May 2025
May 2025
May 2025
May 2025
Dec 2024
Dec 2024
Dec 2024
Dec 2024
Dec 2024
Dec 2024
Dec 2024
May 2024
May 2024
May 2024
May 2024
May 2024
May 2024
Dec 2023
Dec 2023
Dec 2023
Dec 2023
Dec 2023
Dec 2023
Dec 2022
Dec 2022
Dec 2022
Dec 2022
2022 - Summer
2022 - Summer
May 2026
May 2026
May 2026
May 2026
May 2026
May 2026
Sep 2026
Sep 2026
Sep 2026
Sep 2026
Aug 2025
Aug 2025
Aug 2025
Aug 2025
Aug 2025
May 2025
May 2025
May 2025
May 2025
May 2025
May 2025
May 2025
Dec 2024
Dec 2024
Dec 2024
Dec 2024
Dec 2024
May 2024
May 2024
May 2024
May 2024
May 2024
May 2024
May 2024
Dec 2023
May 2023
May 2023
May 2023
May 2023
May 2023
May 2023
Dec 2022
Dec 2022
Dec 2022
Dec 2022
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
2022 - Summer
Dec 2019
Dec 2019
Dec 2019
Dec 2019
Dec 2019
Dec 2018
Dec 2018
Dec 2018
Questions? Email contact@munotes.in
Done!