Course File structure and Marks distribution

1. Discrete Structure
Course Information:
Course Title: Discrete Structure
Course Code: CS-302
Credit Hours: 3(3-0)
Program: BSIT, BSCS
Session: 2019-21
Semester: 2nd
Resource Person: Dr. Ayesha Hakim, Mr. Adnan Altaf, Mr. Muhammad Ashad Baloch.
Contact Information : ayesha.hakim@mnsuam.edu.pk , adnan.altaf@mnsuam.edu.pk,
Ashad5765@gmail.com
Course Introduction:
This course will enable the students to: Apply formal logic proofs and/or informal, but rigorous,
logical reasoning to real problems, such as predicting the behavior of software or solving problems
such as puzzles. Demonstrate comprehension of discrete structures and their relevance within the
context of computer science, in the areas of data structures and algorithms, in particular. Apply
discrete structures into other computing problems such as formal specification, verification,
databases, artificial intelligence, and cryptography.
Learning Objectives:
This course will enable the students to:
 Apply formal logic proofs and/or informal, but rigorous, logical reasoning to real problems,
such as predicting the behavior of software or solving problems such as puzzles.
 Demonstrate comprehension of discrete structures and their relevance within the context of
computer science, in the areas of data structures and algorithms, in particular.
 Apply discrete structures into other computing problems such as formal specification,
verification, databases, artificial intelligence, and cryptography.
Evaluation:
Mid-Term Examination (a combination of online quizzes / assignments) 30%
Final Examination (as decided by the University) 50%
Class participation/attendance/assignments/activity 20%

2. 2
Grading policy:
Course Pre-requisites:
 None
Course Requirement or Rules:
Several rules or subject requirements are mentioned as follows:
 Students are required to visit their course related WhatsApp Group, Facebook Page, Google
classroom (GC)/LMS as per given schedule of the course. Participants should regularly check
their subject related accounts and respond accordingly as PPT slides with audio narration shall
be shared by the course instructor in GC/LMS.
 The course instructor shall generate different activities on Google Classroom/LMS every week
and setting marks for each activity or marking attendance for those who participate in activity
and absence for those who do not participate. A minimum of 60% attendance is required for a
participant to be eligible to sit in the final examination. All students who secured ≥ 60%
attendance in online classes during this semester will be compensated for internet usage fee in
the next semester.
 Participants should regularly visit the course website on Google classroom/LMS and fully
benefit from this platform. The respective Chairperson/Director QEC would be the part of GC
of this subject.
 In the wake of incidents of students misbehaving or passing inappropriate remarks to the
teacher in online groups, any such issue would be reported to Students Affairs Committee, who
will take appropriate action against the concerned students after inquiry within 24 hours.
 Students may withdraw from a course if they are facing severe issue of internet connectivity
or related issues. The course shall be offered in the relevant semester free of cost.

3. 3
Text Books or Other Required Reading Material:
1. Trembley, J. P. and R. Manohar.1997. Discrete Mathematical Structure with Application to
Computer Science. 2nd
Ed. McGraw-Hill, New Dehli, India.
2. Richard, J. B.2018. Discrete Mathematics. 7th
Ed. Prentice Hall, New York, NY, USA.
3. Kenneth H. R. and K.Krithivasan. 2013. Discrete Mathematics and its Applications. 7th
Ed.
McGraw-Hill, Singapore.
Teaching Methodology:
Lectures, Problem-based learning
Key Dates:
Following are the tentative key dates for the given course:
Sr. No. Enrolment Spring Semester 2020 February 12-19,2020
1. Commencement of Classes 20-2-2020
2. Commencement of Online Classes 18-3-2020
3. Assignment 1 due Week 1
4. Assignment 2 due Week 2
5. Assignment 3 due Week 4
6. Activity 2 due Week 6
7. Mid Examination Week 9 or as per policy of the University
8. Assignment 4 due Week 12
9. Students’ presentations Week 16/17
10. Final Examination Week 18 or as per policy of the University
11. Result Declaration As announced by the Office of Controller
Examination
Time and Venue:
Day Time Venue
Thursday 03.00 p.m. – 05.00 p.m. Google classroom
(https://classroom.google.com/c/NTM5MjI3MjI1OTha)
Live Session (Google Meet), WhatsApp Group,
Facebook Group

4. 4
Lesson Plan:
Weeks Topics covered Recommended
Reading
Week 1
Mathematical reasoning: introduction to logic,
propositional, Negation disjunction and conjunction;
Implication. Translation.
Lec01 slides
Assignment No. 1
due
Chapter 1
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and its
Applications. 7th
Edition.
Week 2 Propositional Logic, Compound propositions, Constructing
the truth table, Computer representation of True and False,
Applications of propositional logic, Translation, Tautology,
Contradiction and Contingency, Logical equivalence.
Lec 02 slides
Chapter 1
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and its
Applications. 7th
Edition.
Assignment No. 2
due
Week 3 Predicate logic, Important logical equivalences, Compound
statements in predicate logic, Quantifiers, Universal
quantifier, Existential quantifier
Lec 03 slides
Chapter 1
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and its
Applications. 7th
Edition.
Week 4 Arguments, Valid and Invalid Arguments,
Mathematical induction
Lec 04 slides
Chapter 5
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013.Discrete
Mathematics and its

5. 5
Applications. 7th
Edition.
Assignment No. 3
due
Week 5 Formal and informal proofs, Theorems and proofs, Special
case: equivalences, Rules of inference, Proofs using rules of
inference, Methods of proving theorems, direct and indirect
proof, Proof by contradiction, Trivial proofs, Proof by cases,
Proof of equivalences, Proofs with quantifiers, Divisibility
and Modular Arithmetic, Integer Representations and
Algorithms
Lec 05 (a) slides,
Lec 05 (b) slides
Chapter 1, 4
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 6 Set theory, Paradoxes in set theory
Set, Important sets in discrete math, Russell’s paradox,
Equality, Special sets, Venn diagrams, Subset, Empty
set/Subset properties, A proper subset, Cardinality, Infinite
set, Power set, Cartesian product, Set operations, Disjoint
sets, Cardinality of the set union
Lec06 slides
Chapter 2
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 7 Functions
Functions, Injective function, Surjective function, Bijective
functions, Functions on real numbers, Increasing and
decreasing functions, Identity function, Inverse functions,
Composition of functions, Range versus Codomain, Images
of Sets under Functions, Visualizing Floor & Ceiling
Lec07 slides
Chapter 2
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 8 Boolean Logics
Basic logic gates, NOT, AND, OR gate, DE Morgan’s
Theorem on Gates, Combine gates, Construct the logic table
for these circuits, Gang circuits in sequence, Different
Version of Full Adder, The full adder, Boolean Algebra
Theorems, DE Morgan’s Theorem, Boolean Functions,
Algebraic Manipulation, Complement of a Function,
Canonical Forms
Lec08 slides
Chapter 12
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.

6. 6
Week 9 MID-TERM EXAMINATION (As advised by university)
Week 10 Trees
Trees, Application of trees, Rooted trees, M-ary tree, Binary
trees, General Tree v.s. Binary Tree, Represent Algebraic
Expressions using Binary Tree
Lec10(a and b)
slides
Chapter 11
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 11
Minimum Spanning Trees
Algorithm Characteristics, Prim’s Algorithm, Kruskal’s
Algorithm
Lec11 slides
Chapter 11
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 12 Graphs
Basic types of graphs: Undirected graphs, Directed graphs,
Bipartite graphs, Complete bipartite graphs, Subgraphs,
Union of the graphs, Adjacency matrices, Graph
isomorphism, Connectivity in the graphs, paths
Lec12 slides
Chapter 10
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 13 Graph Operations and Representation
Graph Operations and Representation, Path problems.
Connectedness problems, Spanning tree problems,
Connected Graph, Cycles And Connectedness, Spanning
Tree, Adjacency Matrix, Adjacency Lists, Linked
Adjacency Lists, Array Adjacency Lists -Practical
Examples
Lec13 slides
Chapter 10
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 14 Planar and Non-Planar Graphs
Planar and Non-Planar Graphs, Isomorphic, Subgraph,
Super graph, Subdivision, Kuratowski Reduction Theorem,
Peterson Graph, Euler Path and Circuit, Hamilton Path and
Circuit
Lec 14 slides
Chapter 10
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete

7. 7
Mathematics and
its Applications. 7th
Edition.
Week 15 Relations, Matrices, identity, inverse, Matrix transpose,
Symmetric matrix, Zero-one matrix, Join and meet of
matrices
Lec 15 slides
Chapter 9
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week
16/17
Cramer's Rule
Cramer's Rule, Coefficient Matrices, Cramer’s Rule for 2x2
System , pigeonhole principle.
Lec 16 slides
Chapter 6,9
Book: Kenneth H.
Rosen and
K.Krithivasan.
2013. Discrete
Mathematics and
its Applications. 7th
Edition.
Week 18 FINAL-TERM EXAMINATION
As advised by
university
Assignments
Assignment No. 1: Construct a Truth Tables for each of these Compound proposition
i. (p ∨ ¬q) → (p ∧ q)
ii. ~ p  (q  ~ r)
iii. (pq)  ~ (pq)
Assignment No. 2:
1. Show that (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
2. Are the statements ( p ∧ q ) ∨ r and p ∧( q ∨ r ) logically equivalent?
3. Let p, q, and r be the propositions
p : Grizzly bears have been seen in the area.
q : Hiking is safe on the trail.
r : Berries are ripe along the trail.
Write these propositions using p, q, and r and logical
connectives (including negations).
a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.
b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries
are ripe along the trail.

8. 8
c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not
been seen in the area
Assignment No. 3:
Q1: Consider this argument
If I read my text, I will understand how to do my homework.
I understand how to do my homework.
Therefore, I read my text
Q2: Use a truth table to determine if this argument is valid or invalid. Include a clear explanation
Q3: Consider this argument
My pet is a cat or my pet is a dog.
My pet is not a dog.
Therefore my pet is a cat
PPTs and Handouts
The narrated PPTs / notes / handouts has been uploaded for the students on Google classroom/LMS
as per online class schedule.