3. Let A = {1, 5, 7, 11}. Show that (A, *) is a group, where * is a binary operator defined as x * y = (x ⋅ y) mod 24. Determine the identity and the inverse of each element. 4. Consider the group A in Exercise 3, a. Prove or disprove that A has a subgroup of order 2. b. Prove or disprove that A has a subgroup of order 3.

Answers

Answer 1
Answer:

Answer:

To show that (A, *) is a group, we need to verify four conditions: closure, associativity, identity, and inverses.

1. Closure: For any x, y in A, x * y = (x ⋅ y) mod 24. Since the product of any two elements in A is also in A, closure is satisfied.

2. Associativity: The binary operator * is associative if (x * y) * z = x * (y * z) for all x, y, z in A. Since multiplication and modulo operations are associative, the binary operator * is also associative.

3. Identity: An identity element e in A should satisfy x * e = e * x = x for all x in A. Let's check each element in A:

1 * 1 = (1 ⋅ 1) mod 24 = 1 mod 24 = 1 (not the identity)

5 * 5 = (5 ⋅ 5) mod 24 = 25 mod 24 = 1 (not the identity)

7 * 7 = (7 ⋅ 7) mod 24 = 49 mod 24 = 1 (not the identity)

11 * 11 = (11 ⋅ 11) mod 24 = 121 mod 24 = 1 (not the identity)

None of the elements in A satisfy the condition for an identity element, so (A, *) does not have an identity element.

4. Inverses: For each element x in A, there should exist an element y in A such that x * y = y * x = e, where e is the identity element. Since (A, *) does not have an identity element, it also does not have inverses.

Therefore, (A, *) does not form a group.

For exercise 4:

a. To prove that A has a subgroup of order 2, we need to find two elements in A whose binary operation results in the identity element (which we determined does not exist). Therefore, A does not have a subgroup of order 2.

b. To prove that A has a subgroup of order 3, we need to find three elements in A whose binary operation results in the identity element (which we determined does not exist). Therefore, A does not have a subgroup of order 3.


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Which major NIMS Component describes systems and methods that help to ensure that incident personnel and other decision makers have the means and information they need to make and communicate decisions?

Answers

Answer:

1.Communication Management

2.Information Management

Explanation:

NIMS has introduced COMMUNICATION management system that determines if the decision makers has the ways to communicate decisions. It has standards that defines the ways that can be used by the personnel to communicate the decisions in a better and efficient manner.

NIMS has also a system which is primarily introduced to check the the personnel has the information to make and communicate decisions called Information management. Again, it also has the templates that defines that how information should be spread considering the confidentiality of the information.

[True/False] Mainframes, unlike microcomputers, allow users unlimited and flexible access to computing power.

Answers

Answer:

The given statement is "False".

Explanation:

Mainframes computer are also known big iron computer basically Mainframe computer is used by the big organization when the organization needs to work in the high-level project. The mainframe has big data processing. It is highly used in critical applications such as ERP(Enterprise resource planning).

A mainframe computer is not a flexible computer also they are not potable .microcomputers, are more flexible computers we can easily work on the microcomputers.

So the given statement is False.

Design an information flyer about South Africa's driving regulations that will be given to the contestant of The Awesome Race 2016 who will be driving the 4by4 vehicles. include SIX facts on the flyer.

Answers

Below are six facts that you might include in your flyer regarding Driving Regulation in South Africa:

1. The minimum age required for a driver must be 18.
2. Blood-Alcohol level must be below 0.05%
3. Using of mobile phones while driving is strictly prohibited.
4. Always wear your seat-belts.
5. You must drive on the left side of the road.
6. International driver's license is required when renting a car.

Which features would work well for text entered into cells? Check all that apply.thesaurus
spelling
autosum
average
find
replace

Answers

Answer: A,B,E,F, thesaurus, spelling, find, replace

Explanation:

took it on Edge.

Answer:

A B E F

Explanation:

Write a method named lastFirst that accepts a string as its parameter representing a person's first and last name. The method should return the person's last name followed by the first initial and a period. For example, the call lastFirst("Marla Singer") should return "Singer, M." . You may assume that the string passed consists of exactly two words separated by a single space.

Answers

I'm going to assume this is Java, because you said "method" meaning it will be some sort of object oriented language, and Java's really common. Here would be the full program, but you can just take the method out isolated if you need it.

package lastname;

public class LastName {

   public static void main(String[] args) {

       // Example usage:

       String name = LastName.lastName("Garrett Acord");

       System.out.println(name);

       // Output: Acord G.

   }

   public static String lastName(String fullName)

   {

       String[] splitName = fullName.split(" ");

       return String.format("%s %s.", splitName[1], splitName[0].substring(0,1) );

       

   }

   

}

Your program must define and call the following function that returns the number of times the input character appears in the input string. int CountCharacters(char userChar, string userString)

Answers

Answer:

The program to this question can be given as:

Program:

#include <iostream>  //header file

using namespace std;  //using name space.

int CountCharacters(char userChar,string userString) //define function.

{    

int count = 0;  //define variable

for (int i=0;i<userString.length();i++) //loop

if (userString[i]==userChar)  //if block

count++;  //increment the value.

return count;  //return value.

}

int main()  //main method.

{

   string userString= "Clanguage";  //define variable and assign value.

   char userChar = 'a';   //define variable and assign value.

   cout << CountCharacters(userChar,userString);  //calling function and print value.  

   return 0;  

}

Output:

2

Explanation:

  • In the above C++ programming language program we define a function that is "CountCharacters". Inside function parameters, we pass two parameters that are "userChar and userString". The userChar is a char variable that holds single character value and userString is a string variable that holds a string value.
  • In the function, we define an integer variable that is "count". This variable counts the match value and returns its value.
  • To counts values, we define a loop in a loop we use if statement that counts the value that how many time it occurs in a string value and return its value.
  • In the main method, we define these variables ("userChar and userString") and assign values that are "a and Clanguage " and call the function and print function return value.