An implementation of a queue Q, using two stacks S1 and S2, is given below:void insert(Q, x) {   push (S1, x);}  void delete(Q){   if(stack-empty(S2)) then      if(stack-empty(S1)) then {          print(“Q is empty”);          return;      }      else while (!(stack-empty(S1))){          x=pop(S1);          push(S2,x);      }   x=pop(S2);}Let n insert and m (<=n) delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n?n+m <= x < 2n and 2m <= y <= n+mn+m <= x < 2n and 2m<= y <= 2n2m <= x < 2n and 2m <= y <= n+m2m <= x <2n and 2m <= y <= 2n

The correct answer is "n+m <= x < 2n and 2m<= y <= 2n".

Here's why:

• For every insert operation, we perform one push operation on S1. So, for n insert operations, we perform n push operations.
• For every delete operation, if S2 is empty, we pop all elements from S1 and push them into S2. In the worst case, this can happen for every delete operation. So, for m delete operations, we can perform at most n additional push operations and at most n additional pop operations.
• Therefore, the total number of push operations x is at least n+m (for the n insert and m delete operations) and less than 2n (since we can perform at most n additional push operations).
• Similarly, the total number of pop operations y is at least 2m (for the m delete operations and the at most m additional pop operations during the delete operations) and at most 2n (since we can perform at most n additional pop operations).

So, the statement "n+m <= x < 2n and 2m<= y <= 2n" is true for all m and n.