MATH 2305 Discrete Mathematics
Homework 1
(Textbook, p. 12-15. Exercises)
1. Which of these sentences are propositions? What are the truth values of those that are propositions?
a) Boston is a capital of Massachusetts.
b) Miami is a capital of Florida.
c)
MATH 2305 Discrete Mathematics
Homework 4
(Textbook, pp. 125-126, Exercises)
1. List the elements of these sets
a) cfw_x | x is a square of an integer and x<100
b) cfw_x | x is an integer such that x 2 = 2
2. Determine whether each of these pairs of sets
COSC 2305 Discrete Mathematics
Homework 3
(Textbook, pp. 46-47; p. 61, Exercises)
1. Let P ( x) be the following function determined in the computer program written in some high level
language:
Function P ( x)
if
( ( x > 1) ( x < 5) )
then P( x) = true
el
MATH 2305 Discrete Mathematics
Homework 2
(Textbook, p. 14-16; p. 34-35, Exercises)
1. Construct a truth table for each of these compound propositions
a) p p
b) p ( p q )
c) ( p q ) q
d) p p
e) ( p q ) ( p q )
2. What is the value of x after each of the f
MATH 2305 Discrete Mathematics
Homework 5
(Textbook, pp. 136-138, Exercises)
1. Let A=cfw_1, 2, 3, 4, 5 and B=cfw_0, 3, 6
Find
a) A B
b) A B
c) A B
d) B A
2. Find the sets A and B =
if A B
cfw_1,5, 7,8= cfw_2,10= cfw_3, 6,9
; B A
; A B
3. Draw the Venn di
MATH 2305 Discrete Mathematics
Homework 6
1. Compute the Cartesian product for each of the given sets A and B
a) A a, b; B
= cfw_= cfw_x, y, z
b) A 3, 4,5; B
= cfw_= cfw_1, 2,3
2. Let A be the set of people living in Texarkana. Consider the following rela
MATH 2305 Discrete Mathematics
Homework 10 (exercises pp. 396-398, 405-407, 421-423)
1. There are 4 major auto routes from Boston to Detroit and 6 from Detroit to Los Angeles. How many
major auto routes are there from Boston to Los Angeles via Detroit?
2.
MATH 2305 Discrete Mathematics
Homework 10 (exercises pp. 244-245, 292-293)
1. Which of the following are true?
a)
b)
c)
d)
1897 2200 mod101
7 15 mod11
101 19 mod 5
9 5 mod 8
2. Evaluate the following
a)
b)
c)
d)
[ 7 ] + [ 9 ] in Z 3
[ 7 ] [ 9 ] in Z 3
[
MATH 2305 Discrete Mathematics
Homework 8 (exercises pp. 244-245)
1. Let a, b, and c be integers. Prove that if a | b , then c Z : a | bc .
2. Let a, b, and c be integers. Prove that if a | b , and b | c then a | c .
3. What are the quotient and reminder
MATH 2305 Discrete Mathematics
Homework 7
1. Determine whether f is a function from the set of all bit strings S to the set of integers Z if f ( s ), s S
is the smallest integer i such that the ith bit of s is 0 and f ( s ) = 0 when s is the empty string