UNIT IS: Multiple Choice Questions
Lectures in Discrete Mathematics, Course 1, Bender/Williamson
Review Questions
Multiple Choice Questions for Review
In each case there is one correct answer (given at the end of the problem set). Try
to work the problem

[5] CL-5: The last line of Example 2 should capitalize North and South.
[5] CL-5: In the last sentence of Example 3, word should be name.
[27] CL-27: The running head should be justied right, not centered.
*[27] CL-27: Exercise 3-6: Should say An example

Basic Concepts in Graph Theory
UNIT GT: Multiple Choice Questions
Lectures in Discrete Mathematics, Course 2, Bender/Williamson
Multiple Choice Questions for Review
Some of the following questions assume that you have done the exercises.
1. Indicate which

A Short Course in Discrete Mathematics
errata as of 11/8/2006
[page numbers] in Dover edition.
More important errors are marked with an asterisk.
[8] BF-8: In Exercise 1.2, statements should be statement.
[15] BF-15: In the middle of the paragraph that st

partial order
Partially Ordered Set (Poset)
A relation R on a set A is called
a partial ordering or partial
order if it is reflexive, antisymmetric, and transitive. Set
A together with a partial
ordering R is called a partially
ordered set, and is denoted

Rules of inferences open
propositions with quantifiers
x : A(x) C(x)
x : C(x) M(x)
x : A(x)M(x)
Rules of inferences open
propositions with quantifiers
x : A(x) C(x)
x : C(x) M(x)
x : A(x)M(x)
Rules of inferences open
propositions with quantifiers
x :

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
INSTRUCTION DIVISION
FIRST SEMESTER 2014-15
COURSE HANDOUT(PART-II)
Ausgust 1, 2014
In addition to Part-I (General Handout for all courses appended to the Timetable) this portion gives furthe

Representing Relations
special way to represent relations:
With a zero-one matrix.
R is a relation from A = cfw_u1, u2, , um
to C=cfw_q1, q2, , qn
Represented by the matrix MR
=[mij]mn
mij = 1 if (ui, qj) R
mij = 0 if (ui, qj) R
Example
A = cfw_1, -1,

Logic
Logic = the study of correct
reasoning
Sentences
Sentences are usually classified as
declarative, exclamatory, interrogative
or imperative. We confine our attention
to those declarative sentences to
which we assign one and only one of
its truth val

Lattices and boolean
algebra
Properties of lattices
Before proving a number of properties of
lattices we recall the meaning of x y
and xy
(i) xx y & yx y i.e x y is an upper
bound of x &y.
(ii) If xz & yz then x yz
i.e x y is least upper bound of x &
y x

BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
INSTRUCTION DIVISION
FIRST SEMESTER 2013-14
Proposed COURSE HANDOUT (PART-II)
In addition to Part-I (General Handout for all courses appended to the Timetable) this portion
gives further specific details reg

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE-PILANI, K. K. Birla
GOA CAMPUS
FIRST SEMESTER 2013-2014
Course Handout (Part II)
Date: 01/08/2013
In addition to part-I (General Handout for all courses appended to the time table), this portion
gives further spec

BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
K K BIRLA GOA CAMPUS
FIRST SEMESTER 2012-13
Course Handout (Part II)
Dated: 25/07/2013
In addition to part-I, (General Handout for all courses appended to the time table) this
portion gives further specific

UNIT DT: Multiple Choice Questions
Lectures in Discrete Mathematics, Course 2, Bender/Williamson
Review Questions
Multiple Choice Questions for Review
1. In each case, two permutations on 6 are listed. In which case is the rst permutation
less than the se

UNIT Fn:Multiple Choice Questions
Lectures in Discrete Mathematics, Course 2, Bender/Williamson
Review Questions
Multiple Choice Questions for Review
1. In each case some information is given about a function. In which case is the information not sucient

UNIT EO: Multiple Choice Questions
Lectures in Discrete Mathematics, Course 1, Bender/Williamson
Equivalence and Order
Multiple Choice Questions for Review
In each case there is one correct answer (given at the end of the problem set). Try
to work the pro

Arithmetic, Logic and Numbers
With and Introduction to Cryptography
Unit BF: Boolean Functions and Computer Arithmetic
Edward A. Bender
S. Gill Williamson
c Edward A. Bender & S. Gill Williamson 2010. All rights reserved.
Preface
The material in this unit

Arithmetic, Logic and Numbers
With and Introduction to Cryptography
Unit Lo: Logic
Edward A. Bender
S. Gill Williamson
c Edward A. Bender & S. Gill Williamson 2010. All rights reserved.
Preface
The material in this unit of study was, over several years, p

Solutions for Boolean Functions and Computer Arithmetic
BF-1.1 The idea of this problem is to show how English phrases are translated into logical
expressions.
(a) f s. In English, but is and with an underlying message: The use of but
in this way often (b

UNIT BF: Multiple Choice Questions
Lectures in Discrete Mathematics, Course 1, Bender/Williamson
Review Questions
Multiple Choice Questions for Review
In each case there is one correct answer (given at the end of the problem set). Try
to work the problem

Sets, Equivalence and Order
With an Introduction to Sequences and Series
Unit SF: Sets and Functions
Edward A. Bender
S. Gill Williamson
c Edward A. Bender & S. Gill Williamson 2010. All rights reserved.
Preface
The material in this unit of study was, ove

UNIT Lo: Multiple Choice Questions
Lectures in Discrete Mathematics, Course 1, Bender/Williamson,
Review Questions
Multiple Choice Questions for Review
In each case there is one correct answer (given at the end of the problem set). Try
to work the problem

Arithmetic, Logic and Numbers
With an Introduction to Cryptography
Unit NT: Number Theory and Cryptography
Edward A. Bender
S. Gill Williamson
c Edward A. Bender & S. Gill Williamson 2010. All rights reserved.
Preface
The material in this unit of study wa

Number Theory and Cryptography
Multiple Choice Questions for Review
UNIT NT: Multiple Choice Questions
Lectures in Discrete Mathematics,
Course 1, Bender/Williamson
In each case there is one correct answer (given at the end of the problem set). Try
to wor

UNIT SF: Multiple Choice Questions
Lectures in Discrete Mathematics, Course 1, Bender/Williamson
Review Questions
Multiple Choice Questions for Review
In each case there is one correct answer (given at the end of the problem set). Try
to work the problem

Sets, Equivalence and Order
With an Introduction to Sequences and Series
Unit IS: Induction, Sequences and Series
Edward A. Bender
S. Gill Williamson
c Edward A. Bender & S. Gill Williamson 2010. All rights reserved.
Preface
The material in this unit of s

Notation Index
(there exists)
(for all)
Fn-4
Fn-4
(such that) Fn-4
Bn (Bell numbers) CL-27
s t (equivalence relation) GT-5
n
k
(binomial coecient) CL-15
n
m1 ,m2 ,.
(multinomial
coecient) CL-20
Probability notation
X (expectation, or
mean) Fn-24
(X, Y

Sets, Equivalence and Order
With an Introduction to Sequences and Series
Unit EO: Equivalence and Order
Edward A. Bender
S. Gill Williamson
c Edward A. Bender & S. Gill Williamson 2010. All rights reserved.
Preface
The material in this unit of study was,