public static void main(String[] args) { int n = Integer.parseInt(args[0]); assert (n > 0); // Assertion 1 assert (n + (n-1)/9 == n + (n-1)/9) && (n > 0); // Assertion 2 int b = n; assert (b + (n-1)/9 == n + (n-1)/9) && (n > 0); // Assertion 3 int c = n; assert (b + (c-1)/9 == n + (n-1)/9) && (c > 0); // Assertion 4 while (c >= 10) { assert (b + (c-1)/9 == n + (n-1)/9) && (c > 0) && (c >= 10); // Assertion 5 assert ((b+1) + ((c-9)-1)/9 == n + (n-1)/9) && (c-9 > 0); // Assertion 6 c = c - 9; assert ((b+1) + (c-1)/9 == n + (n-1)/9) && (c > 0); // Assertion 7 b = b + 1; assert (b + (c-1)/9 == n + (n-1)/9) && (c > 0); // Assertion 8 } assert (b + (c-1)/9 == n + (n-1)/9) && (c > 0) && (c < 10); // Assertion 9 assert (b == n + (n-1)/9); // Assertion 10 System.out.printf("b = %d ", b); } }

Given the Assertion 2 holds, argue that Assertion 3 holds after executing the statement int b = n;

Given the Assertion 3 holds, argue that Assertion 4 holds after executing the statement int c = n;

Given the Assertion 4 holds, suppose the while condition is evaluated to true, argue that Assertion 5.