Math 280
Strategies of Proof
Homework Solutions
2.1 Predicates and Quantied Statements
Fall 2013
3. Given the following propositional functions with domain Z, the set of all integers
p(n) : n is positive.
q(n) : n is even.
r(n) : n is a perfect square.
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Math 280
Strategies of Proof
Homework Solutions
3.4 Proving Conditional Statements I: Direct Proofs
Fall 2015
1. Let f : ( 1, 0) ! R be the function defined by f (x) = 2
x2 for each x 2 ( 1, 0).
(a) Show that f is injective.
In symbolic form, we need to s
Math 280
Homework Solutions
3.5 Proofs in Set Theory
Strategies of Proof
Spring 2014
3. Disprove: For all sets A, B, and C, if A [ C B [ C, then A B.
This statement has symbolic form
8A 8B 8C [(A [ C B [ C) ! (A B)].
To disprove this statement, we need to
Math 280
Strategies of Proof
Spring 2016
Homework Assignment
Directions for Writing Proofs
You must follow the directions for writing proofs contained in section 3.1 of the class notes (see pages
6667). In particular, here are some guidelines you should b
Math 280 Class Notes 3.10 Epsilon-Delta Proofs
Strategies of Proof
Fall 2007
The denitions of the limit of an innite sequence and of the limit of a function are among the most important in mathematics. They are also one of the greatest sources of diculty
Math 280
Strategies of Proof
Homework Solutions
3.2 Proving Existentially Quantied Statements
Spring 2014
2. Disprove: For all integers n, 5n + 1 is odd.
This has symbolic form
(8n 2 Z) [5n + 1 is odd].
To disprove this, we need to nd a counterexample. Ch
Math 280 Strategies of Proof Class Notes 2.1 Propositional Functions and Quantied Statements
Fall 2007
In Chapter 1, we dened a statement, or a proposition, as a declarative sentence which has a denite truth value. Most sentences which we encounter in mat
Math 280
Strategies of Proof
Spring 2016
Exam 2 Information
Date: Wednesday, March 23
Exam 2 will cover the following sections:
Chapter 2, Sections 2, 3
Chapter 3, Sections 1, 2, 3
You will need to bring a large (8 12 11) blue book to the exam.
For all pr
Math 280
Strategies of Proof
Spring 2016
Exam 1 Information
Date: Wednesday, February 24
Exam 1 will cover the following sections:
Chapter 1, Sections 1, 2, 3
Chapter 2, Section 1
You will need to bring a large (8 12 11) blue book to the exam.
Exam 1 Revi
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Math 280
CHAPTER 12 and 13 REVIEW
1.
Find the equation of the sphere one of whose diameters has endpoints (5, 2, 9) and (3, 6, 1) .
2.
Let A(1 1, 1), B(1, 4, 3), C(2, 5, 1), D(1, 3, 7) . Find the following:
,
a.
b.
The angle between AB and AC
The line thr
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Math 280 Name
TEST #2A
Chapter 14
Work carefully. You must show all work in a clearly organized manner in the space provided in order to receive
full credit.
1. (8 pts) Find and sketch the domain of f(x,y) = arccosty).
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2. (10 pts) Determine whether th
Math 280 Name
TEST #23
Chapter 14
Work carefully. You must show all work in a clearly organized manner in the space provided in order to receive
full credit.
1. (8 pts) Find and sketch the domain of f(X,y) = arcsin(xy).
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Math 280
Strategies of Proof
Fall 2016
Exam 2 Information
Date: Wednesday, October 19
Exam 2 will cover the following sections:
Chapter 2, Section 3
Chapter 3, Sections 1, 2, 3, 4
You will need to bring a large (8 12 11) blue book to the exam.
For all pro
Math 280
Strategies of Proof
Homework Solutions
2.1 Propositional Functions and Quantified Statements
Fall 2016
1. Consider the propositional functions
p(x) : x2 x 12 = (x
q(x) : x is odd.
r(x) : x > 0.
4)(x + 3) = 0.
where the domain of the variable x is
Math 280
Homework Solutions
2.3 Sets
Strategies of Proof
Fall 2016
1. The following sets are written using the rule method. For each set, identify the domain and rule and
write the set using the list method.
(a) A = cfw_n 2 N | (9p) (9q) [n = pq ^ (p is p
Math 280
Strategies of Proof
Fall 2016
Homework Assignment
Directions for Writing Proofs
You must follow the directions for writing proofs contained in section 3.1 of the class notes (see pages
6667). In particular, here are some guidelines you should be
Math 280
Strategies of Proof
Fall 2016
Exam 1 Information
Date: Wednesday, September 21
Exam 1 will cover the following sections:
Chapter 1, Sections 1, 2, 3
Chapter 2, Sections 1, 2
You will need to bring a large (8 12 11) blue book to the exam.
Exam 1 R