(5.) Consider the unit circle C with equation x + y = 1 in the plane....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(5.) Consider the unit circle C with equation x² + y² = 1 in the plane. Thus C = {(x, y) ERX R: x² + y² = 1}. Define a relation ~ on C as follows: For (x, y) E C, (x, y) is related to itself and to its antipodal point (-x, -y). In symbols, (x, y)~ (x, y); (x, y) ~(-x, y). (a) Show that is an equivalence relation. (b) Think of C as a rubber band and imagine gluing together the equivalent antipodal points of C. Describe the resulting figure. (Much more will be said on this topic in Chapter 7.) (5.) Consider the unit circle C with equation x² + y² = 1 in the plane. Thus C = {(x, y) ERX R: x² + y² = 1}. Define a relation ~ on C as follows: For (x, y) E C, (x, y) is related to itself and to its antipodal point (-x, -y). In symbols, (x, y)~ (x, y); (x, y) ~(-x, y). (a) Show that is an equivalence relation. (b) Think of C as a rubber band and imagine gluing together the equivalent antipodal points of C. Describe the resulting figure. (Much more will be said on this topic in Chapter 7.)
Expert Answer:
Answer rating: 100% (QA)
Solution consider the unit circle x y 1 in the plane c xy EIRXIR ayt1 Define a a that is every it se... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
Show that any equivalence relation on a set X partitions X.
-
Consider the equivalence relation from Example 2, namely, R = {(x, y) | x y is an integer}. a) What is the equivalence class of 1 for this equivalence relation? b) What is the equivalence class of...
-
Imagine a unit circle in which a point is rotated A radians counterclockwise about the origin from the positive x-axis. Copy this table and record the x-coordinate and y-coordinate for each angle....
-
You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. But you're worried that only 100 students will show up to vote. How often will the underdog...
-
Roundtree Company, a U.S. corporation with customers in several foreign countries, had the following selected transactions for 2011 and 2012. 2011 Apr. 8 Sold merchandise to Salinas & Sons of Mexico...
-
Suppose that the subjects in an experiment are reused. For example, each person in a taste test samples every product. Are these data suitable for a one-way ANOVA?
-
The adjusted trial balance for Sparkys Electrical Supply, Inc., as of November 30, 2010, is presented next: Requirements 1. Prepare the multi-step income statement for November for Sparkys Electrical...
-
As part of your audit of the Abba Company accounts payable function, your audit program includes a test of controls addressing the company policy requiring that all vouchers be properly approved. You...
-
Appropriately selecting a financial destination and mapping an efficient route to get there requires the use of which specific type of human capital? money profile money self money identity financial...
-
Hypothesis Testing for the Population Proportion Use a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and paste values or type values, as you will...
-
A firm intends to choose the best offer (or ranking of the offers) from the set of proposals submitted by potential contractors. Two experts evaluate five proposals using several criteria. In order...
-
How does the interplay between mitochondrial dynamics, including fission and fusion, affect cellular metabolism and apoptosis, and what role do these processes play in the pathophysiology of diseases...
-
1. Determine and confirm purchasing requirements for at least six (6) of the goods listed in the knowledge evidence. 2.Make purchase arrangements for the goods to meet different: End product...
-
Which of the following accurately describes something that occurs with the 2- component regulatory system? O Binding of a signal molecule to the sensor causes a phosphate group to fall off the...
-
2. Consciously experienced pleasure or displeasure is called reward. C. affect. d. a. b. drive. incentive.
-
what is the effect to domestic investors of the country allows foreign investors to own up to 100% of domestic enterprises in the country?
-
What is another path or method to add a user defined exception to the code listed below? Is it as simple as just changing the variables? import java.util.Scanner; import java.util.ArrayList; import...
-
Hardin Services Co. experienced the following events in 2016: 1. Provided services on account. 2. Collected cash for accounts receivable. 3. Attempted to collect an account and, when unsuccessful,...
-
A certain organism possesses a pair of each of 5 different genes (which we will designate by the first 5 letters of the English alphabet). Each gene appears in 2 forms (which we designate by...
-
Extend the definition of conditional independence to more than 2 events.
-
In Laplaces rule of succession (Example 5e), show that if the first n flips all result in heads, then the conditional probability that the next m flips also result in all heads is (n + 1)/(n + m + 1).
-
What are the gears used for intersecting shafts?
-
A pinion of involute profile has 25 teeth and \(150 \mathrm{~mm}\) pitch circle diameter. It drives a rack. The addendum of both pinion and rack is \(6.25 \mathrm{~mm}\). Calculate the least pressure...
-
Which gears are used for non-parallel and non-intersecting shafts?
Study smarter with the SolutionInn App