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University of Barishal

Department of Computer Science and Engineering

Final Exam

Course Title: Discrete Mathematics (CSE-1203)

Semester: 2nd | Session: 22-23

Time: 180 minutes | Marks: 60.00

Course Teacher: Md. Rashid Al Asif

Exam Date: December 2, 2024

View 106 Topic-wise Questions for this Course

N.B.: Answer any Five questions out of the followings. All parts of each question must be answered consecutively. Right side of the question shows the maximum marks.

1.

a)

Verify that validating of the following inference. If one person is more successful than another, then he has worked harder to deserve success. X has not worked harder than Y. Therefore, X is not more successful than Y.

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Topics: Modus Tollens , Propositional Logic Solution is Coming!
4 Marks
b)

Define logically Equivalences of compound proposition. Show that this implication is a tautology by using truth table. [(p → q) ∩ (q → r)] → (p → r)

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Topics: Propositional Logic , Tautology , Truth Table Solution is Coming!
4 Marks
c) What are the differences between 'one to one' and 'onto' function? Provide examples.

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Topics: N/A Solution is Coming!
4 Marks
2.

a) Define predicates and quantifiers with examples.

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Topics: N/A Solution is Coming!
3 Marks
b) How can this English sentence be translated into logical expression? "You can't ride the roller coaster if you're under 4 feet tall, unless you're over 16."

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Topics: N/A Solution is Coming!
4 Marks
c) Let Q(x) denotes the statement "x=x+1". What is the truth value of the qualification Ǝ xQ(x), where domain consists of all real numbers?

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Topics: N/A Solution is Coming!
5 Marks
3.

a) What do you know about algorithm complexity? Analyze the time complexity of the following algorithm:

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Topics: Time Complexity Solution is Coming!
5 Marks
b)

Show that ∀x (P(x)^Q(x)) and ∀x P(x)^∀x Q(x) are logically equivalent.

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Topics: Predicate Logic , Quantifiers , Universal Quantifier Solution is Coming!
4 Marks
c) For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive with explanation. i) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} ii) {(2, 4), (4, 2)}

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Topics: N/A Solution is Coming!
3 Marks
4.

a) Suppose here, r> k and the degree of q(n) is r. Prove that q(n) = O(n^r).

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Topics: N/A Solution is Coming!
4 Marks
b)

Represent with Venn diagram the relationship i) AUB = {x|x∈A V x∈B} ii) A∩B= {x|x∈A Ʌ x∈B)

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Topics: Intersection of Sets , Union of Sets , Venn Diagram Solution is Coming!
4 Marks
c) Let A = {1, 2, 3, 4), B = {3, 4, 5, 6}, and C = {2, 4, 6, 8} Prove or disprove: AU(B∩C) = (AUB)∩(AUC)

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Topics: N/A Solution is Coming!
4 Marks
5.

a) A university offers the following courses: 38 courses in Mathematics and 42 courses in Computer Science. If a student can choose either a Mathematics course or a Computer Science course, how many choices does the student have in total? Explain your reasoning using the Sum Rule.

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Topics: N/A Solution is Coming!
3 Marks
b) A library has two sections: i) Fiction Section: 8 books ii) Non-fiction Section: 10 books If a person wants to borrow one book from either section and one magazine (there are 6 magazines available), how many total choices does the person have?

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Topics: N/A Solution is Coming!
4 Marks
c) Explain how the generalized pigeonhole principle can be used to show that among any 91 integers, there are at least ten that end with the same digit.

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Topics: N/A Solution is Coming!
5 Marks
6.

a)

"A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?"

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Topics: Bayes’ Theorem , Conditional Probability , Discrete Probability Solution is Coming!
4 Marks
b)

In how many ways can we select three students from a group of five students to stand in line for a picture? In how many ways can we arrange all five of these students in a line for a picture?

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Topics: Combinatorics , Factorial Notation , Permutations and Arrangements Solution is Coming!
4 Marks
c) A committee of 4 members is to be formed from a group of 10 people. i) How many different committees can be formed if there are no restrictions? ii) Suppose the group consists of 6 men and 4 women. How many committees can be formed if the committee must include exactly 2 men and 2 women?

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Topics: N/A Solution is Coming!
4 Marks
7.

a) Consider the following undirected graph G: It has 6 vertices, with degrees 2, 3, 3, 2, 4, and 4, respectively. i) Determine whether the graph G has an Eulerian circuit. Justify your answer using the necessary and sufficient condition for Eulerian circuits. ii) If G does not have an Eulerian circuit, explain whether it has an Eulerian path, and if so, identify the starting and ending vertices.

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Topics: N/A Solution is Coming!
6 Marks
b) Let G be a 4-regular connected planar graph having 16 edges. Find the number of regions of G.

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Topics: N/A Solution is Coming!
2 Marks
c)

What is planner graph? Draw the planner graph of the given graph.

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Topics: Euler’s Formula , Graph Theory Solution is Coming!
4 Marks
8.

a) Illustrate how Kruskal's algorithm and Prim's algorithm are used to find a minimum spanning tree, using a weighted graph with at least eight vertices and 15 edges.

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Topics: N/A Solution is Coming!
5 Marks
b)

Define Handshaking Theorem/Lemma. Find the in-degree and out-degree of each vertex in the following graph with directed edges.

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Topics: Directed Graphs (Digraphs) , Graph Theory , Handshaking Theorem / Lemma Solution is Coming!
4 Marks
c) Define Isomorphic graph and Bipartite graph with example.

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Topics: N/A Solution is Coming!
3 Marks
View 106 Topic-wise Questions for this Course

Contributors of this Question:

Role Name Date
Prepared By (Teacher): Md. Rashid Al Asif Dec. 2, 2024
Uploaded By: Dip Dey Dec. 2, 2024, 4:21 p.m.
Converted By (Img/PDF to Text): Baishakhi Bir Nov. 22, 2025, 10:39 a.m.
Reviewed By: Obaydul Hasan Nayeem Nov. 22, 2025, 12:12 p.m.
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