MATH 211: Worksheet 8.1
Name_
November 17, 2014
1. The congruence modulo 4 relation, R, is defined from
For all integers m and n,
a. Is
13R1?
Is
12 R16?
Is
31,19 R ?
to
as follows:
mRn 4 m n
Is
1,9 R ?
13 1 = 12
12 16 = -4
31 19 = 12
-1 9 = -10
4 div

MATH 211: Worksheet 2.3
Name_
Write each of the following arguments in symbolic form, and state whether each is
valid or invalid. Justify by stating which argument form is used or which error is
made.
1. It will either rain or snow tomorrow. Let p = It wi

MATH 211: Worksheet 2.2 & 2.3
Name_
1. Rewrite the following statement as a conjunction of two if-then statements:
This integer is even if and only if it equals twice some integer.
If this integer is even, then it equals twice some integer, and if this in

MATH 211: Worksheet 3.3
Name_
1. Let
G x, y be x 2 y.
Which of the following statements are true and which
are false?
a.
True.9 > 4.
b.
G 3, 4
2. Let
D E 2, 1, 0,1, 2
1 1
G ,
2 2
False. < .
.
a. Explain why the following statement is true:
x in D
such t

Worksheet 4.2
Name_
1. The following numbers are rational. Write each as a ratio of integers.
a. 3.5106
b. 0.4848484848
(a) 3.5106 is an exact decimal,
3
5106 35106
10000 10000
(b) Let x = 0.484848484848. Then 100x = 48.4848484848 and
100x x = 99x = 48.48

MATH 211: Worksheet 3.1
Name_
1. A box of doughnuts consists of three regular glazed, two lemon filled, four
chocolate, one strawberry filled, one maple glazed, and one apple filled.
Determine which of the following statements are true and which are false

MATH 211 Worksheet 6.2 & 6.3
For each of the following statements, write what you will assume and what you
must show to complete a proof of the statement.
1. Given
A C and B D.
Assume:
Show:
Since
x A B
A C and B D.
x C D
x A B
by definition of union we c

Worksheet 6.1
Name_
1. Let
A 1, 4,7,10,13,16
,
B 1,3,5, 7
and
C 2, 4, 6,8,10
Find each of the
following:
a.
=cfw_1, 3, 4, 5, 7, 10, 13, 16
A B
b.
c.
AC
B A
= cfw_4, 10
= cfw_3, 5
2. Let the universal set be the set of real numbers, and let
,
B x 0 x 3
a.

MATH 211: Worksheet 4.3
1. Does
2. Is
7 56?
Name_
Yes, because 56 =
6m 2m 10
3m 15
2
7 8
divisible by 4? Yes.
6m 2m 10 12m2 60 4 3m2 15
Since
is a product and sum of integers, it is an integer, making the expression a multiple
of 4.
3. Prove the followi

MATH 211: Worksheet 5.1
Name_
1. Find the explicit formula for the
The terms have the forms
20 , 21 , 22 , 23 , 24 ,.
4
4
1
2
m 0
m
k 1
2
, or
n0
m
2
k
k 1
k
for
1, 2, 2 2 , 23 , 2 4 ,.
1 1 1 1 1
1 1 1 1 1
31
1 2 3 4
0
2 2 2 2 2
1 2 4 8 16
16
3. Find

MATH 211: Worksheet 8.3
Name_
The following relations are equivalence relations. Find the equivalence
classes for each.
1.
A a , b, c , d
and
R a, a , b, b , b, d , c, c , d , b , d , d
a a
b b, d d
c c
2.
A 1, 2,3, 4,., 20
R is defined on A as foll

MTH 287 Project, Spring 2016 (due Wednesday July 27, 2016, 4:30pm)
Description: A discrete mathematics course teaches more than a set of skills and
mathematical facts. It teaches the scientific way of thinking, helping students to
think logically and anal