MATH355 Discrete Math / Quiz 6 / 2 Mar 2015
Name KE. 2 12 points
1. Base b numeration systems. Convert (2035),ight to base ten. Show work.
2.33+ o-gzv 392W 5.2 s was + o -+ m + 5 = 6053)
2. Integer division
a. Prove: Let a, b, and c be integers with a at
MATH355 Discrete Math / Quiz 8 / 1 Apr 2015
Name K E"? 12 points Box
This is a take-home quiz.
0 It is due at the beginning of class on Monday, April 6.
oYou'may use your own class-notes, textbook, other books, and previous quizzes.
0 Do not get help from
MATH355 Discrete Math / Quiz 41/ 11 Feb 2015
Name - K5 Y 12 points Box
1. (7 points) Congruence modulo m
a. List three positive integers and three negative integers that are congruent to 5 modulo 8.
we-27,*fi-).II 3.? .5) /3) 2:) 26) 37J .,
7 b. According
MATH355 Discrete Math / Quiz 1 / 12 Jan 2015
Name x_< g 2 12 points
1. (4 points) Write the converse and contrapositive of the following conditional proposition:
If n2 is even, then H is even.
converse: Of ,4 M W) W n1 ML. oemh
. . _ .z m n 2-. (4; o"
con
MATH355 Discrete Math / Quiz 9 / 13 Apr 2015
Name K E 2 12 points
1. (8 points) Complete the denitions, where A and B are sets.
a.Afunctionf:A > Bis one-to-one ifand only if. . V15) e A) 430g) :5?th A X, we.
b.AfunctionF:A ~+BmapsAontoBifandonlyif. V L B
MATH355 Discrete Math / Quiz 3 / 28 Jan 2015
Name 5 E z 12 points Box
1. (3 points) Write the negation of each proposition.
a.p>q P A?-
b. All prime integers are odd. meal/e 15 at. Prime ~Hmi [5 even .
c. Vx e R (x is rational > x2 is rational)
3956 R (x
MATH355 Discrete Math / Quiz 7 f/ 25 Mar 2015
Name K as; 12 points Box
1. Complete the denitions, where A and B are sets.
a. A is a subset of B, denoted A 5 8 , if and only if . . .
For sevw-y %, iva/Jc my: xe; 8*.
b. The Cartesian product of A andB is th
#2#
MATH355 Discrete Math / Quiz 2 / 14 Jan 2015
Name &5 z 12 points
1. (2 points) Write the contrapositive of the following conditional proposition:
If a matrix A is invertible, then det(A) = 1.
Di ,6; any a. Mm Mme, alarmw 1,
2. (4 points) Complete the
Proofs
1. Choose Method
a. Let x be a element with a certain property something is true.
2. Direct
a. Assume p then q.
3. Contraposition
a. We will use the contrapositive so assume not q then not p.
4. Biconditi
Cardinality
Finite: If there are exactly n distinct elements in S where n is non negative
Same cardinality: one to one corr
Countable: finite or same cardinality as set of positive int
UAi = for some i
Div & Mod
Divides (Divisor): Let a&b be integers where a=/= 0. We say a divides b iff b=ak for
some integer k.
Modulo: Let a&b be integers and let m be a positive integer. We say a is congruent to
b mod
Worksheet # 1: Review
1. (MA 113 Exam 1, Problem 1, Spring 2007). Find the equation of the line that passes through (1, 2) and is parallel to the line 4x + 2y = 11. Put your answer in y = mx + b form. 2. Find the slope, x-intercept, and y-intercept of the
CHAPTER 2: METHODS OF PROOF Section 2.1: BASIC PROOFS WITH QUANTIFIERS Existence Proofs Our first goal is to prove a statement of the form (x) P (x). There are two types of existence proofs: Constructive Proofs of Existence: (a) One type of constructive p
Question 1
4 out of 4 points
Five
measurements are
taken and are:
59.5", 61.33",
60.55", 61.00",
59.8". Find the
likely size of the
chance error in a
single
measurement.
Answer
Selected Answer:
0.6943
Correct Answer:
0.6943
Response
Feedback:
That is cor
die is tossed 5 times. Find the probability that none of the rolls show 4 or more spots.
Answer
Selected Answer:
a.
1/32
Correct Answer:
a.
1/32
Question 2
4 out of 4 points
Find the chance
that if you toss a
pair of dice, you
get 6 for the sum.
Answer
a certain town, there are 40,000 registered voters, of whom 15,000 are Republicans. A survey
organization is about to take a simple random sample of 1,200 registered voters. Find the
expected value for the percentage of Republicans in the sample.
Answer
Math 170 Test #2 Review
DIRECTIONS: Show all steps leading to your answers, including any intermediate results obtained
using a graphing utility.
f ( x + h) f ( x )
1) Use the definition of a derivative f ( x) = lim
to find the derivative of f ( x) = 2 x