Project II: Number Systems
In this section we consider three number systems that are of importance in
applications, namely, the decimal system, the binary system, and the hexadecimal system. Decimal numbers are used in communication among human
beings whe
Review Problems
Problem 3.1
Use modus ponens or modus tollens to fill in the blanks in the argument
below so as to produce valid inferences.
If
p
2 is rational, then
p
2=a
b for some integers a and b:
It is not true that
p
2=a
b for some integers a and b:
Review Problems
Problem 4.1
By finding a counterexample, show that the proposition: \For all positive
integers n and m; m:n _ m + n" is false.
Problem 4.2
Consider the statement
9x 2 IR such that x2 = 2:
Which of the following are equivalent ways of expre
More Methods of Proof
A vacuous proof is a proof of an implication p ! q in which it is shown
that p is false.
Example 9.1
Use the method of vacuous proof to show that if x 2 ; then David is playing
pool.
Solution.
Since the proposition x 2 ; is always fa
Fundamentals of Mathematical
Proofs
In this chapter we discuss some common methods of proof and the standard
terminology that accompanies them.
8 Methods of Direct Proof I
A mathematical system consists of axioms, de_nitions, and unde_ned
terms. An axiom
Project I: Digital Logic Design
In this section we discuss the logic of digital circuits which are considered to
be the basic components of most digital systems, such as electronic computers, electronic phones, tra_c light controls, etc.
The purpose of di
Lecture Notes in Discrete Mathematics
Marcel B. Finan
Arkansas Tech University
c All Rights Reserved
2
Preface
This book is designed for a one semester course in discrete mathematics
for sophomore or junior level students. The text covers the mathematical
Review Problems
Problem 2.1
Rewrite the following proposition in ifthen form: \ this loop will repeat
Exactly N times if it does not contain a stop or a go to."
Problem 2.2
Construct the truth table for the proposition: _ p _ q! R:
Problem 2.3
Construct t
Review Problems
Problem 1.1
Indicate which of the following sentences are propositions.
a. 1,024 is the smallest four-digit number that is perfect square.
b. She is a mathematics major.
c. 128 = 26
d. x = 26:
Problem 1.2
Consider the propositions:
p: Juan