Question

In: Advanced Math

Write the multiplication table for D8. Find the order of each element D8.

Expert Solution

Here, denotes the identity element, is an element of order 4, and is an element of order two that isn't equal to , as in the above presentation.

The row element is multiplied on the left and the column element is multiplied on the right.

Element

Ordee of each element:

Element in terms of and	Geometric description	Order of the element
(identity element)	does nothing, i.e., leaves the square invariant	1
	rotation by angle of (i.e., ) counterclockwise	4
	rotation by angle of (i.e., ), also called a half turn	2
	rotation by angle of (i.e., ) counter-clockwise, or equivalently, by (i.e., ) clockwise	4
	reflection about the diagonal joining vertices "2" and "4"	2
	reflection about the line joining midpoints of opposite sides "14" and "23"	2
	reflection about the diagonal joining vertices "1" and "3"	2
	reflection about the line joining midpoints of opposite sides "12" and "34"	2

Colby Messinger answered 2 years ago

For each group in the following list find the order of each element in the group:...

For each group in the following list find the order of each element in the group: Z12, U(10) and U(12).

Find the product from the multiplication table for the symmetries of an equilateral triangle the new...

Find the product from the multiplication table for the symmetries of an equilateral triangle the new permutation notation to verify each of the following: A) R(240)R3 B) R3R(240) C) R1R3 D) R3R1

Write a Java program that uses nested for loops to print a multiplication table as shown...

Write a Java program that uses nested for loops to print a multiplication table as shown below. Make sure to include the table headings and separators as shown. The values in the body of the table should be computed using the values in the heading e.g. row 1 column 3 is 1 times 3.

Java Program Use for loop 1.) Write a program to display the multiplication table of a...

Java Program Use for loop 1.) Write a program to display the multiplication table of a given integer. Multiplier and number of terms (multiplicand) must be user's input. Sample output: Enter the Multiplier: 5 Enter the number of terms: 3 5x0=0 5x1=5 5x2=10 5x3=15 2 Create a program that will allow the user to input an integer and display the sum of squares from 1 to n. Example, the sum of squares for 10 is as follows: (do not use...

Write a java program of a multiplication table of binary numbers using a 2D array of...

Write a java program of a multiplication table of binary numbers using a 2D array of integers.

Find the order and the inverse of the element in the indicated group. (a) (17, 4)...

Find the order and the inverse of the element in the indicated group. (a) (17, 4) ∈ Z-18 × Z-18 (b) (10,(1 4 5),(1 2)(3 4 5)) ∈ Z-12 × A-5 × S-5 (c) (35, 18, 30, 4) ∈ Z-45 × Z-26 × Z-35 × Z-38

Write a loop that subtracts 1 from each element in lowerScores. If the element was already...

Write a loop that subtracts 1 from each element in lowerScores. If the element was already 0 or negative, assign 0 to the element. Ex: lowerScores = {5, 0, 2, -3} becomes {4, 0, 1, 0}. please bold the solution import java.util.Scanner; public class StudentScores { public static void main (String [] args) { Scanner scnr = new Scanner(System.in); final int SCORES_SIZE = 4; int[] lowerScores = new int[SCORES_SIZE]; int i; for (i = 0; i < lowerScores.length; ++i) {...

In C. Write a loop that subtracts 1 from each element in lowerScores. If the element...

In C. Write a loop that subtracts 1 from each element in lowerScores. If the element was already 0 or negative, assign 0 to the element. Ex: lowerScores = {5, 0, 2, -3} becomes {4, 0, 1, 0}.

Find the center of S3 and the centralizer of each element of S3

1. Write down the addition and multiplication table for Z/5Z. All classes should be written in...

1. Write down the addition and multiplication table for Z/5Z. All classes should be written in terms of their canonical representative (unique representative between 0 and 4). 2. Suppose a ≡ a' mod n and b ≡ b' mod n. (a) Show that a + b ≡ a' + b' mod n. (b) Show that a · b ≡ a' · b' mod n. (An important consequence of this exercise is that addition and multiplication define maps Z/nZ × Z/nZ...