Answer: Let S be the subset of the set of ordered pairs of
Chapter 4, Problem 4.3.27(choose chapter or problem)
Let S be the subset of the set of ordered pairs of integers defined recursively by Basis step: (0, 0) E S. Recursive step: If (a , b) E S, then (a , b + 1) E S, (a + 1, b + 1) E S, and (a + 2, b + 1) E S. a) List the elements of S produced by the first four applications of the recursive definition. b) Use strong induction on the number of applications of the recursive step of the definition to show that a 2b whenever (a , b) E S. c) Use structural induction to show that a 2b whenever (a, b) E S.
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