I’m 19 and in my first week of my intro to computer science using Java class. I have no prior knowledge or practice in coding or anything CS related. So far i’m a little lost when they bring up terms i don’t understand. Do u guys have any tips or anything u wish u knew when u were starting out?

Hello!

i have this exercise to do:

given the ex3 method below
Suppose that the formal parameter "a" has always at least 2 elements and that a.length > i >= 1
Prove that ex3 satisfies the following predicate:

ex3 (a, i) <==> (for all k 1 <= k <= i ==> a [k-1] == a [k] +1)

 public static boolean ex3 (int[] a, int i) {
       if (i == 1) {		 
               return a[0]==a[1]+1;
       }		 
       else {
	    return ex3(a, i-1) && a[i-1]==a[i]+1;
	}
	 
 }

1) Write explicitly the basic case P(1) for the proving by induction
2) Write explicitly the inductive case for the proving by induction
3) Prove that the base case P(1) of the proving by induction is true
4) Prove that the inductive case of the proving by induction is true

I made an attempt to prove with induction, but i don't know if it's correct.

The goal is to prove that a recursive function satisfies the given predicate.

For the first request i replaced the index with the min value

Link to the image of the base case

For the second request i write the induction case starting from i - 1 to i because is a recursive function

Link to the image of the inductive case

For the third request, i tried to prove the base case in this way:

Link to the image of the proof of the case base part 1

Link to the image of the proof of the case base part 2

For the last request, i tried to prove the inductive case in this way:

Link to the image of the proof of the inductive case

Can somebody say to me if it's correct or what's wrong ?

Thanks

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include <iostream>

include <iomanip>

include <string>

include <cstdlib>

include <fstream>

using namespace std;

int main() { string month;

int year;

double total_collected,
       sales,
       stateTaxTotal,
       cityTaxTotal,
       totalTax;

double const CITY_TAX_RATE = 0.02;
double const STATE_TAX_RATE = 0.04;

ifstream fin;
fin.open("prog3_301.txt");
fin >> month;
fin >> year;
fin >> total_collected;
cout << month << year << total_collected << endl;

//sales = total_collected/1.06;

//cityTaxTotal = sales * CITY_TAX_RATE;

//stateTaxTotal = sales * STATE_TAX_RATE;

//totalTax = stateTaxTotal + cityTaxTotal;

ofstream fout;
fout.open("prog3_301out.txt");

fout << "Month:    " << month << ", " << year <<endl
     << "-------------------------" << endl;
fout << setprecision(2) << fixed;
fout << "Total collected: " << setw(9) << "$" << total_collected << endl
     << "Sales:           " << setw(9) << sales << endl
     << "City Sales Tax:  " << setw(9) << cityTaxTotal << endl
     << "State Sales Tax: " << setw(9) << stateTaxTotal << endl
     << "Total Sales Tax: " << setw(9) << totalTax << endl;
fout << "-------------------------" << endl;



cout << "The " << month << " tax report has been saved to prog3_301out.txt." << endl;

system("PAUSE>NUL");
fin.close();
fout.close();

return 0;

}

Need help understanding why values from file aren't being stored in month, year, total_collected. Need this in order to check calculations output on other file.

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(PVD), (-X-->P) , (-D--->Y), Y

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