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Each of the following two procedures defines a method for adding two positive integers in terms of the procedures inc, which increments its argument by 1, and dec, which decrements its argument by 1:
(define (plus1 a b)
(if (= a 0)
b
(inc (plus1 (dec a) b))))
(define (plus2 a b)
(plus2 (dec a) (inc b)))) Using the substitution model, illustrate the process generated by each procedure in evaluating (+ 2 5). Are these processes iterative or recursive?
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Show that we can represent pairs of nonnegative integers using only numbers and arithmetic operations if we represent the pair a and b as the integer that is the product 2 a 3 b .
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