1.
Which of the following sentences are logical statements?
1. If x even divides y, then x is a factor of y
Logical Statement
2. If John does well in discrete math, then he will be an excellent programmer
Illogical, no way to infer that he will be a good
1.
Enumerate the elements of the following relations from the set A of positive integers
less than or equal to 10 to the set B of positive integers less than or equal to 30.
1. An element a of A is related to the element b of B if b = 3 a
cfw_(1,3), (2, 6
David McCarty
CMSC 150
1.
Calculate the number of integers divisible by 4 between 50 and 500, inclusive.
Just divide the numbers by 4 and cut out any remainder. E.g.
50
=12 <- the
4
number of integers between 0 and 50 divisible by 4. There are 12 integer
1. Translate the following English sentences into statements of predicate calculus.
a. All programmers enjoy discrete mathematics
X = programmer
E(x) = Enjoys discrete mathematics
(x)E(x)
b. Some integers are not odd
X = integers
N(x) = x is not odd
(x)N(
1.
Enumerate the elements of the following sets:
1. cfw_x: x is an odd positive integer less than 13
cfw_1,3,5,7,9,11
2. cfw_y: y is a positive integer that is a multiple of 4 and greater than 10 but
less than 25
cfw_12,16,20,24
2.
What is the cardinality
1.
2.
Determine whether each of the following functions is 1-to-1 and whether it is onto.
Assume the domain and co-domain is Z, the integers. Explain your answers.
a. f(n) = n / 2, assuming integer division
This function is one-to-one. There are no two or
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
1.
Prove that the difference of two odd integers is even. Give a justification at each
step.
2.
(x) Z, [D(O(x1),O(x2) E]
(hyp) the initial argument.
D(x,y)
O(x)
E
Z
For all odd integers x, y: x y = n, n is an
even integer
x = 2k1+1
y = 2k2+1
(2k1+1)-(2k2+
JesseJoseph
ProfessorSuciu
CMSC150
1. Enumeratetheelementsofthefollowingsets:
a. cfw_x:xisanoddpositiveintegerlessthan13
b. cfw_y:yisapositiveintegerthatisamultipleof4andgreaterthan10butlessthan
25
Solution:
a. x=cfw_1,3,5,7,9,11
b. y=cfw_12,16,20,24
2. W