Using python 3.0 or greater. I need help writing this recursive function.

Question: Write a recursive function (not using loops, global varibles, and conditional operators (+,-,=,<=,==,!=, etc) to for the following definitions.

In other words, make the functions rely on the definitions given and use recursion (can be a bit confusing).

(Three given functions to use in question)

def incr(a):

 '''Returns the next integer after a'''  return a + 1 def zero(a): '''Returns True if a is zero'''  return a == 0 def decr(a): '''Returns the integer before a'''  return a - 1 

(Write the following recursive functions below, by using the functions above.)

I already got the 3 defnintion for the function, but need help writing the recursive for the others.

(Notice how I did not use any +,-,==,=,//,*,etc...becuase they are not allowd in question, only recursion and the functions given.)

def add(a, b): '''Returns the sum of a and b''' # using only incr, decr, zero, and recursion if zero(a) and zero(b): return 0 elif zero(b): return a else: return add(incr(a), decr(b)) def mult(a, b): if zero(b): return 0 else: return add(a ,mult(a, decr(b))) def gt(a, b): '''Returns True if a is an integer greater than b; returns False otherwise''' # using only incr, decr, zero, and recursion if zero(b) and zero(a): return False elif zero(b): return True elif zero(a): return False return gt(decr(a), decr(b))

Help with these Please.

def sub(a, b): '''Returns the difference between a and b.  Only works if b >= 0'''  # using only gt, incr, decr, zero, and recursion  return  def quot(a, b): '''Returns the result of integer division of a by b'''  # using only sub, gt, incr, decr, zero, and recursion  return  def rem(a, b): '''Returns the remainder of integer division of a by b'''  # using only sub, gt, incr, decr, zero, and recursion  return