Question: 3. Structural Induction (5 points) Let S be the subset of the set of ordered pairs of integers defined recursively by: Basis step: (0,0)ES Recursive

3. Structural Induction (5 points) Let S be the subset of

3. Structural Induction (5 points) Let S be the subset of the set of ordered pairs of integers defined recursively by: Basis step: (0,0)ES Recursive step: If (a, b) E S, then (a + 2, b +3) E S and (a +3, b + 2)E S (1) (1 point) List the elements of S produced by the first five applications of the recursive definition 2) (4 points) Use structural induction to show that 5la +b when (a, b) E S (Reminder: 51(a + b)(a + b) = 5k for some k E Z. In other words (a +b) is divisible by 5.)

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