Back to Other Questions [Of this Course]
👁️ 156 views
University of Barishal Logo

University of Barishal

Department of Computer Science and Engineering

Final Exam

Course Title: Discrete Mathematics (CSE-1203)

Semester: 2nd | Session: 21-22

Time: 180 minutes | Marks: 60.00

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)

Define proposition with example. Consider the following sentences and determine which of the following is a proposition or not. (i) Dhaka is the capital of Bangladesh. (ii) 2+3=5 (iii) x+2=11 x+y=y+x, for every pair of real numbers x and y.

Please SUBSCRIBE to view full question

Topics: Propositional Logic Solution is Coming!
5 Marks
b) Construct a truth table for the following compound propositions, (pVq) → (pɅq), where p and q represent arbitrary propositions. Determine whether this compound proposition is tautology, contradiction, or contingency. Justify your answer.

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
3 Marks
c) Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. Let the domain consist of all people. (i) Someone in your class can speak Japanese. (ii) Everyone in your class is friendly. (iii) There is a person in your class who was not born in Jashore. (iv) No student in your class has taken a course in logic programming.

Please SUBSCRIBE to view full question

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

a) Define predicates and quantifiers with examples.

Please SUBSCRIBE to view full question

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

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
c) Using Mathematical induction method show that

Please SUBSCRIBE to view full question

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

a) Show that if A, B and C are sets, then (A ∩B ∩C)'=A'∪ B'∪ C'.

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
b) Show that ∀x.(P(x)ΛQ(x)) and ∀xP(x) Λ ∀xQ(x) are logically equivalent.

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
c) Let A = {0, 1, 2, 3} and define relations R, S and T on A as follows: R= {(0,0), (0,1), (0,3), (1,0), (1, 1), (2,2), (3,0), (3,3)}, S= {(0,0), (0,2), (0,3), (2,3)}, T= {(0, 1), (2, 3)}. i) Is R reflexive? Symmetric? Transitive? ii) Is S reflexive? Symmetric? Transitive?

Please SUBSCRIBE to view full question

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

a) Use rules of inference to show that the hypotheses "If it does not rain or if it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on," "If the sailing race is held, then the trophy will be awarded," and "The trophy was not awarded" imply the conclusion "It rained."

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
b) Prove that, if n is an integer and 3n + 2 is odd, then n is odd?

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
c) Define Argument. Express the statements "Some student in this class has visited Mexico" and "Every student in this class has visited either Canada or Mexico" using predicates and quantifiers.

Please SUBSCRIBE to view full question

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

a) Discuss generalized pigeonhole principle and proof this theorem using proof by contradiction.

Please SUBSCRIBE to view full question

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

Suppose that there are eight runners in a race. The winner receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. How many different ways are there to award to these medals, if all possible outcomes of the race can occur and there no ties?

Please SUBSCRIBE to view full question

Topics: Combinatorics , Factorial Notation , Permutations and Arrangements Solution is Coming!
3 Marks
c) How many bit strings of length 8 contain at least two 1s and at most two 0s?

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
3 Marks
d) Each user on a computer system has a password, which is five to eight characters long, where each character is an uppercase letter or lowercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there?

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
3 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?"

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
5 Marks
b) Let E1 and E2 be events in the sample space S. Then proof the following: P(E1 U E2)=P(E1) + P(E2) - P(E1 ∩ E2)

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
c) What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 2 or 5?

Please SUBSCRIBE to view full question

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

a) A computer company receives 350 applications from college graduates for a job planning a line of new web servers. Suppose that 220 of these applicants majored in CSE, 147 majored in Math, and 51 majored both in CSE and Math. How many of these applicants majored neither in CSE nor in Math.

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
b) Explain Eulerian and Hamiltonian graphs with examples, also draw the graphs of the following: i) Eulerian but not Hamiltonian ii) Hamiltonian but not Eulerian

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
c) What is planner graph? Draw the planner graph of the given simple graph.

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
4 Marks
8.

a) Find all the spanning tree of graph G and find which is the minimal spanning tree of G shown in fig:

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
6 Marks
b) Define Directed Graph. A drawing of the directed graph with vertices a, b, c, d, and e, and edges (a, a), (a, b), (b, c), (b, d), (a, d), (a, e), (e, d), (e, e), (e, a), (d, d), (c, e), (c, a) and (b, e).

Please SUBSCRIBE to view full question

Topics: N/A Solution is Coming!
3 Marks
c) How many 5-digit numbers can be formed by using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 if every number is to start with '40' with no digit repeated?

Please SUBSCRIBE to view full question

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

Contributors of this Question:

Role Name Date
Uploaded By: Onebyzero Edu (Test User) July 27, 2024, 9:52 p.m.
Converted By (Img/PDF to Text): Baishakhi Bir Nov. 24, 2025, 12:23 a.m.
Reviewed By: Obaydul Hasan Nayeem Nov. 24, 2025, 11 a.m.
Back to Other Questions [Of this Course]