Question 2 In this question we consider colorings of the points at the cornersof a square the colors red and green. To make this formal, we label the pointson the corners as in the picture belou.1.43The set of colorings X is the set of functions from {1, 2, 3, 4} to {red, green}.Answer the following questions.1. What is |X|?2. Define two elements f and g of X to be rotationally equivalent if f canbe obtained from g by rotating it by either 0,90, 180 or 270 degrees. Thisis an example of an equivalence relation. The equivalence classes of anequivalence relation on a set Y form a partition of Y. By drawing picturesof the colorings, give a complete description of the partition of X thatcomes from the rotational equivalence relation.3. What is the number of pieces in the partition from the previous problem?How many different colorings are there if we view rotationally equivalentcolorings as the same?4. We say that a rotation by e degrees fixes a coloring f if rotating f by 0gives back f.(a) How many colorings are fixed when rotating by 0 degrees?(b) How many colorings are fixed uwhen rotating by 90 degrees?(c) How many colorings are fixed when rotating by 180 degrees?(d) How many colorings are fixed when rotating by 270 degrees?5. Compute (a +b+c+d) where a, b, c, d are your answers to the parts ofthe previous question. Notice anything interesting?

Answered: Image /qna-images/answer/36d0e2c4-96ff-4bb7-be21-5d45ed09c642.jpg

Question 2 In this question we consider colorings of the points at the corners of a square the colors red and green. To make this formal, we label the points on the corners as in the picture belouw. 1. 4 3 The set of colorings X is the set of functions from {1, 2, 3, 4} to {red, green}. Answer the follouwing questions. 1. What is |X|?

Question 2 In this question we consider colorings of the points at the corners of a square the colors red and green. To make this formal, we label the points on the corners as in the picture belouw. 1. 4 3 The set of colorings X is the set of functions from {1, 2, 3, 4} to {red, green}. Answer the follouwing questions. 1. What is |X|?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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