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vodomira [7]
3 years ago
11

Give an example of a function from N to N that is: Hint: try using absolute value, floor, or ceiling for part (b). (a) one-to-on

e but not onto (b) onto but not one-to-one (c) neither one-to-one nor onto
Computers and Technology
1 answer:
Naily [24]3 years ago
5 0

Answer:

Let f be a function  

a) f(n) = n²  

b) f(n) = n/2  

c) f(n) = 0  

Explanation:  

a) f(n) = n²  

This function is one-to-one function because the square of two different or distinct natural numbers cannot be equal.  

Let a and b are two elements both belong to N i.e. a ∈ N and b ∈ N. Then:

                               f(a) = f(b) ⇒ a² = b² ⇒ a = b  

The function f(n)= n² is not an onto function because not every natural number is a square of a natural number. This means that there is no other natural number that can be squared to result in that natural number.  For example 2 is a natural numbers but not a perfect square and also 24 is a natural number but not a perfect square.  

b) f(n) = n/2  

The above function example is an onto function because every natural number, let’s say n is a natural number that belongs to N, is the image of 2n. For example:

                               f(2n) = [2n/2] = n  

The above function is not one-to-one function because there are certain different natural numbers that have the same value or image. For example:  

When the value of n=1, then

                                  n/2 = [1/2] = [0.5] = 1  

When the value of n=2 then  

                                   n/2 = [2/2] = [1] = 1  

c) f(n) = 0

The above function is neither one-to-one nor onto. In order to depict that a function is not one-to-one there should be two elements in N having same image and the above example is not one to one because every integer has the same image.  The above function example is also not an onto function because every positive integer is not an image of any natural number.

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Sometimes it is hard for some people to say thank you and to rate 5 star when correct so i will you deserve it thanks for adding a correct answer! have a great day!! 
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Create the Following Menu in a loop so the menu will continually show until the user chooses to exit.AddMultiplyExitAdd a value
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Answer:

I have added the code again with the mistakes are corrected please see the comments in code. You have mistake in while loop condition.

#include <iostream>

#include <iomanip>

#include <cmath>

using namespace std;

int options ();

int option1 ();

int option2 ();

int option3 ();

double addition (double num1, double num2);

double multiplication (double num1, double num2);

int main()

{  

jump:

int option = 0;  

cout << "1. Add" << endl;

cout << "2. Multiply" << endl;

cout << "3. Exit" << endl;

 cout << "Enter option 1 for addition, option 2 for multiplication, or option 3 to exit" "Enter an option: ";

  cin >> option;

   switch (option)  

{  

case 1:option1;  

int option1 ();

{  

double num1 = 0;  

double num2 = 0;

// void int key = 0;  

cout << " Enter a number: ";  

cin >> num1;  

cout<< " Enter a second number: ";  

cin >> num2;  

double sum = addition(num1, num2);  

cout << " Sum is: " << sum <<endl;

 } break;  

 case 2: option2;  

 int option2 ();

 {  

 double num1 = 0;  

 double num2 = 0;

 cout << " Enter a number:";

 cin >> num1;

 cout << " Enter a second number: ";

 cin >> num2;

 double product = multiplication(num1, num2);

  cout << " Product is: " << product << endl;

  //system("cls");

  }  

  break;

   case 3: option3;  

   int option3();

    {

 return 0;

 }  

 break;  

 default: cout << " Invalid number entered: ";

 }

 //do {main();}

 //while (option < 3); //you have mistake in this loop please have a look

 while (option<3)

 {

  goto jump;

 }

 

 }

 double addition(double num1, double num2)

 {

  return num1 + num2;

  }

 double multiplication(double num1, double num2)

 {

  return num1*num2;

  }

Explanation:

You can also do this by using goto statement in switch case and menu will be repeated until the user not select to exit and now it will work with the loop as well.

I hope it will help you!

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3 years ago
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