( { ih ih ion the set { how many total orderings can be defined on set with elementsexplain your answer define an adt for set of integers (remember that set has no concept of duplicate elementsand has no concept of orderyour adt should consist of the functions that can be performed on set to control its membershipcheck the sizecheck if given element is in the setand so on each function should be defined in terms of its input and output define an adt for bag of integers (remember that bag may contain duplicatesand has no concept of orderyour adt should consist of the functions that can be performed on bag to control its membershipcheck the sizecheck if given element is in the setand so on each function should be defined in terms of its input and output define an adt for sequence of integers (remember that sequence may contain duplicatesand supports the concept of position for its elementsyour adt should consist of the functions that can be performed on sequence to control its membershipcheck the sizecheck if given element is in the setand so on each function should be defined in terms of its input and output an investor places $ , into stock fund years later the account has value of $ , using logarithms and anti-logarithmspresent formula for calculating the average annual rate of increase then use your formula to determine the average annual growth rate for this fund rewrite the factorial function of section without using recursion rewrite the for loop for the random permutation generator of section as recursive function here is simple recursive function to compute the fibonacci sequence/recursive fibonacci generator static long fibr(int /fibr( is the largest value that fits in long assert ( &( < " out of range"if (( = |( = )return /base case return fibr( - fibr( - )/recursive call this algorithm turns out to be very slowcalling fibr total of fib(ntimes contrast this with the following iterative algorithm