(a) Prove or disprove carefully and in detail: (i) is transitive and (ii) is symmetric.

(b) Assume n is a positive integer.

Algorithm A(n: int)

int z = 0;

for (int i = 0; i < n ; i++)

{

for (int j = 0 ; j < n ; j++)

{

int temp = i + j ;

int z = z + temp;

}

}

System.out.printlin(z) ;

What is the input size for Algorithm A? Analyze carefully the time complexity of A in terms of the input size. Show all steps. Is A a polynomial time algorithm? Justify your answer

Please provide with good explanation