scheme - DrRacket procedure body help (boolean-odd? x)

Question

An iterative version of odd? for non-negative integer arguments can be written using and, or, and not. To do so, you have to take advantage of the fact that and and or are special forms that evaluate their arguments in order from left to right, exiting as soon as the value is determined. Write (boolean-odd? x) without using if or cond, but using and, or, not (boolean) instead. You may use + and -, but do not use quotient, remainder, /, etc.

Answer 1

A number is even if two divides it evenly, and odd if there if there is a remainder of one. In general, when you divide a number k by a number n, the remainder is one element of the set {0,1,…n-1}. You can generalize your question by asking whether, when k is divided by n, the remainder is in some privileged set of remainder values. Since this is almost certainly homework, I do not want to provide a direct answer to your question, but I'll answer this more general version, without sticking to the constraints of using only and and or.

(define (special-remainder? k n special-remainders)
  (if (< k n)
      (member k special-remainders)
      (special-remainder? (- k n) special-remainders)))

This special-remainder? recursively divides k by n until a remainder less than n is found. Then n is tested for its specialness. In the case that you're considering, you'll be able to eliminate special-remainders, because you don't need (member k special-remainders). Since you only have one special remainder, you can just check whether k is that special remainder.