MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 9
Student Guide
Lesson 9: Definitions and Biconditionals, Part 2
Have you ever tried to figure out if a statement is a definition? What about this statement? A cow i
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 3
Student Guide
Lesson 3: Conditional Statements, Part 1
In the game Telephone, you whisper a phrase to a friend. The friend whispers it to the next person and so on
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 7
Student Guide
Lesson 7: Compound Statements and Indirect Proof, Part 2
Ms. Nickel was on trial for burglary. Her lawyer told the jury she couldnt have committed th
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 10
Student Guide
Lesson 10: Algebraic Logic, Part 1
Suppose you are an attorney arguing a case before a judge or a jury. It is your job to make a conjecture (my
clie
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 8
Student Guide
Lesson 8: Definitions and Biconditionals, Part 1
When you look at a tree, you see an organism that appears to be one unit, but in reality it consists
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 2
Student Guide
Lesson 2: Reasoning, Arguments, and Proof, Part 2
While searching the Internet for possible extracurricular activities, you come across a site promot
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 5
Student Guide
Lesson 5: Conditional Statements, Part 3
Have you ever felt a sense of belonging? You are probably part of many thingsyour circle of friends, your fa
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 1 : An Introduction | Lesson 2
Student Guide
Lesson 2: Basic Geometric Terms and Definitions, Part 1
In geometry, we start with the most basic terms: point, line, and plane. These terms are so basic that w
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 16
Student Guide
Lesson 16: Methods of Proof and Logic Unit Test
In Unit 2, you learned that reasoning is a deliberate process that progresses logically from idea to
M
142: H
#1
Curtis Tekell
Prof. Kate Poirier
February 11, 2013
Exercise 1. Consider with its standard metric 0 , (, ) =
.
(a) Prove that the standard metric on is indeed a metric.
(b) Consider with its standard metric. Show that () = ( , + ).
(c) Show th
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Math 142, Spring 2013. HW5 Solutions
1. Let A X be connected.
a) If A is closed then A = A so the statement is trivial. Assume that A = A and suppose
that A is not connected. Then, there are nonempty open subsets U, V A such that
U V = and A = U V . Let A
Math 142, Spring 2013. HW7 Solutions
2. a) Denote the constant map with with domain I , R and image cfw_0 I , R, by f0 , by abuse
of notation; hence, f (x) = 0, for each x I , R. Dene the homotopies
H1 : I I I ; (t, x) (1 t)x,
H2 : I R R ; (t, x) (1 t)x.
Math 142, Spring 2013. HW2 Solutions
3. a) Let A X , with X a topological space. Then, A is the intersection of every closed set
that contains A,
A=
F
AF
F closed in X
Thus, as this is an arbitrary intersection of closed sets it must be a closed set (by t
Math 142, Spring 2013. HW3 Solutions
3. a) Write
S = Q1 Q2 Q3 Q4 ,
where Q1 is the east quadrant in S, Q2 is the north quadrant in S, Q3 is the west quadrant
in S, Q4 is the south quadrant in S. For example, we have
Q1 = cfw_(x, y ) S | |x| |y |, x 0
and
Math 142, Spring 2013. HW8 Solutions
4. Consider a homomorphism f : 1 (S1 , 1) 1 (S 1 , 1); this morphism is completely determined by the value f (1) (since, for n > 0, f (n) = f (1 + 1 + . + 1) = f (1) + . + f (1) and
f (1) = f (1), so f (n) = f (1) . f
MTH204A: Honors Geometry (ELI-PUBLISHABLE) | Unit 2 : Methods of Proof and Logic | Lesson 4
Student Guide
Lesson 4: Conditional Statements, Part 2
There is no formula for solving a crime. Instead, detectives and other law enforcement officers sift through