Daffodil International University
Department of Computer Science and Engineering Faculty of Science & Information Technology
Midterm Examination, Summer 2021 @ DIU Blended Learning Center Course Code: CSE236 (Day), Course Title: Math for Computer Science
Level: 2 Term: 3 Section: A
Instructor: SL Modality: Open Book Exam Date: Tuesday, 16 November, 2021 Time: 09:00am-11:30am
Two and half hours (2:30) to support online open/case study based assessment Marks: 25
Q.N.01 .
Consider the following sketch given below. Assume that an area contains entities (four- footed animals) that satisfy the characteristics mentioned by the arrow head labeling the area. Also assume that the situation portrayed in the sketch is true.With respect to the situation portrayed below answer (i), (ii), and (iii).
[2*3=
6]
Q.N.02 .
a) Take the last alphabets of your last name and the last four digits of student ID as two separate sets. Then find the value of the union and cartesian product of the sets.
b) State the converse, contrapositive, and inverse of each of these conditional statements with an explanation.
i) If it rains today, then I will drive to work.
ii) If |x| = x, then x ≥ 0.
iii) If n is greater than 3, then n2 is greater than 9.
[3+3]
x is a four-footed animal.
R(x): x runs fast I (x): x is intelligent
M (x): x likes meat D(x): x likes to dominate jungle (i) Identify the area ¬ R(x) ˄ I(x) ˄ ¬ M(x)
(ii) Determine True or False with explanation:
x R(x) ˄ ¬ M(x)
(iii) Determine True or False with explanation:
x R(x) ˄ M(x) ˄ I(x) → D(x)
Q.N.03 .
“Manhattan Prep” is an American test preparation company. It offers both on-site and virtual preparatory programs for students worldwide. Its curriculum is designed around a
"content-based" approach that teaches the material covered on the exam rather than solely focusing on test-beating strategies.
a) To use Manhattan prep, a user has to register himself/herself and set login credentials. It requires users to create passwords from the word ‘Manhattan’. If each password must have at least 6 letters and no repeated letters are allowed, how many different passwords are possible?
b) Manhattan Prep provides various services. A user can take any of these 4 services like GRE, GMAT, LSAT, EA. How many different combinations are possible from which a user can benefitted?
[3+3]
Q.N.04 .
Which function the following diagrams represent? Explain your answer.
[2]
Q.N.05 .
Suppose that we have an infinite ladder, and we want to know whether we can reach every step on this ladder. We know two things:
i) We can reach the first rung of the ladder.
ii) If we can reach a particular rung of the ladder, then we can reach the next rung.
Can we conclude that we can reach every rung? Prove your answer mathematically.
[5]
Best of Luck!
a b c d
x y z
A f B
a b c d
z x y m
A f B
