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.
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.
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.
spelling
autosum
average
find
replace
Answer: A,B,E,F, thesaurus, spelling, find, replace
Explanation:
took it on Edge.
Answer:
A B E F
Explanation:
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) );
}
}
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: