For this question answer individual parts. (a) The McCarthy 91 function is defined using the rule: M(n) = n ? 10 if n > 100 M(M(n + 11)) if n ? 100 By successively using the defining rule for M(n), find M(87) Answer:

(b) A set is well ordered if every nonempty subset of this set has a least element. Determine if the set of integers greater than -100 is well ordered. Answer:

(c) Find the flaw with the following proof that every postage of three cents or more can be formed using just three-cent and four-cent stamps. Basis Step: We can form postage of three cents with a single three-cent stamp and we can form postage of four cents using a single four-cent stamp. Inductive Step: Assume that we can form postage of j cents for all nonnegative integers j with j ? k using just three-cent and four-cent stamps. We can then form postage of k + 1 cents by replacing one three-cent stamp with a four-cent stamp or by replacing two four-cent stamps with three three-cent stamps. Answer: