Question

Hello, If anyone would be so kind as to help me out with a solution in either Java or C++ please and thank you !!!

CS 278 Lab3: Quantified statements Write a program that does the following. It should take as a user input ten different integers and store them in a length ten integer array (with no repeated entries). The domain D is the set of entries in this array. Recall that if the domain is a finite set of elements (a, a, ..., a.), then: Vx P(x) = P(a) A P(a) A ... A P(a) and 3x P(x) = P(a) v P(a.) V ... v P(a). Your program should evaluate the truth/falsity of the following statements with respect to the domain D. For each statement it should print the statement label and its truth value. Statements: a) Vx (if x<0 then x is even ). b) x (if x<0 then x is even ). c) x (x<0 and x is even ). d) x ( either x is of the form one more than a multiple of three or x is of the form one more than a multiple of two ). Your program must compute truth-values correctly for all possible inputs. Example: An output produced by your program may look like the following user input is in green): Please enter 10 different integers: 35-360-517-18 a) is False b) is True c) is False d) is False Note: There is no typo in the sample output. Answer to b) is True. We can take x=3. Then, 3<0 is False. Therefore, statement "if 3<0 then 3 is even" is True. Implementation details: You may assume that the user input is always correct that is, the user always enters integers with no repeated entries). You do not need to check the user input for correctness. • You may use the functions you implemented in Lab 2 for “if... then ..." (), "and" («), and "either ... or..." (V). What to submit: Submit the source code of your program using Canvas. If you write your program in a programming language other than Java, then submit instructions on how to compile and run your program on CS machines.

Answer 1

Java code for he above question is provided below. Please comment if any doubt.

DomainProgram.java

package domainprogram;

import java.util.Scanner;

public class DomainProgram {
    public static void main(String[] args) {
        int[] arr=new int[10];
        Scanner sc=new Scanner(System.in);
      
        // Read 10 integers to array
        System.out.print("Please enter 10 different integers:");
        for(int i=0;i<10;i++)
        {
            arr[i]=sc.nextInt();
        }
      
        // a) For all x, ifx<0 then x is even
        boolean result=true;
        for(int i=0;i<10;i++)
        {
            int x= arr[i];
            // If first condition is false the result is true
            // If first condition is true and the second condition is false it return false
            // If first condition is true and the second condition is also true it return true
            if(x<0)
            {
                if(x%2!=0)
                {
                    result=false;
                    break;
                }
            }
        }
        if(result)
            System.out.println("a) is True");
        else
           System.out.println("a) is False");
      
        // b) There exist some x such that, if x<0 then x is even
        result=false;
        for(int i=0;i<10;i++)
        {
            int x= arr[i];
            // if first condition is true
            if(x<0)
            {
                // If second condition is also true
                if(x%2==0)
                {
                    result=true;
                    break;
                }
            }
            // if first conditionis false
            else
            {
                result=true;
                break;
            }
        }
        if(result)
            System.out.println("b) is True");
        else
           System.out.println("b) is False");
      
        // c) There exist some x such that, x<0 and x is even
        result=false;
        for(int i=0;i<10;i++)
        {
            int x= arr[i];
            // Check both conditions are true
            if(x<0 && (x%2==0))
            {
                result=true;
                break;
            }
        }
        if(result)
            System.out.println("c) is True");
        else
           System.out.println("c) is False");
      
        // d) For all x such that, x is one more than multiple of three
        // or x is of the form one more than a multiple of two
        result=true;
        for(int i=0;i<10;i++)
        {
            int x= arr[i];
            // Check any of the condition is false
            if((x%3!=1)&& (x%2!=1))
            {
                result=false;
                break;
            }
        }
        if(result)
            System.out.println("d) is True");
        else
           System.out.println("d) is False");
    }
}

Output:

Output - Domain Program (run) x A run: Please enter 10 different integers: 3 5 -3 6 0 -5 1 7 -1 8 a) is Falsel b) is True c) is False d) is False BUILD SUCCESSFUL (total time: 37 seconds)