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Construst a natural deduction... All natural deductions are to be done using onl

ID: 3859460 • Letter: C

Question

Construst a natural deduction...

All natural deductions are to be done using only ND rules on the ND Rule Sheet. Remember to number each line and justify each line after the initial assumptions. For any auxiliary assumption justify it by indicating for what purpose you are introducing that assumption, e.g., A/Superset I. i. Construct a ND to show that the following is a valid sentence. (This derivation can be done in 11.) (J L) Superset ((I & L) Superset [(I Superset K) Superset ((K & J) S)]) ii. Construct a ND to show that the following set is inconsistent. {A B, ~ B, (~ C D) Superset ~ A, ~ C} iii. Show that ND determines the following to be equivalent. ~ (~ A Superset ~ B) ~ A & B

Explanation / Answer

/*

Calculate Circle Area using Java Example

This Calculate Circle Area using Java Example shows how to calculate

area of circle using it's radius.

*/

import java.io.BufferedReader;

import java.io.IOException;

import java.io.InputStreamReader;

public class CalculateCircleAreaExample {

  public static void main(String[] args) {

  

  int radius = 0;

  System.out.println("Please enter radius of a circle");

  

  try

  {

  //get the radius from console

  BufferedReader br = newBufferedReader(new InputStreamReader(System.in));

radius =Integer.parseInt(br.readLine());

  }

  //if invalid value was entered

  catch(NumberFormatException ne)

  {

  System.out.println("Invalid radius value" + ne);

  System.exit(0);

  }

  catch(IOException ioe)

  {

  System.out.println("IO Error :" + ioe);

  System.exit(0);

  }

  

  /*

* Area of a circle is

* pi * r * r

* where r is a radius of a circle.

*/

  

  //NOTE : use Math.PI constant to get value of pi

  double area = Math.PI * radius * radius;

  

  System.out.println("Area of a circle is " +area);

  }

}

/*

Output of Calculate Circle Area using Java Example would be

Please enter radius of a circle

19

Area of a circle is 1134.1149479459152

*/

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