Suppose S is a recursively defined set, defined by - the number 1 is in S - if n is in S, then so is 3n + 2 - if n is in S, then so is 5n - 1 - if n is in S, then so is n + 7. Suppose you want to prove using structural induction that all members of S have a certain property. What do you have to prove in the base step?

Question

Mathematics

Laylah Acevedo

19 September, 06:14

Suppose S is a recursively defined set, defined by - the number 1 is in S - if n is in S, then so is 3n + 2 - if n is in S, then so is 5n - 1 - if n is in S, then so is n + 7. Suppose you want to prove using structural induction that all members of S have a certain property. What do you have to prove in the base step?

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Answers (1)

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Annabelle Baird · Answer 1

See answer below

Step-by-step explanation:

Using structural induction, we would have to prove that 1 and all the numbers derived from this fact, have the property.

That is to say, we would have to prove that

1, 3*1+2, 5*1-1 and 1+7 = {1, 4, 5, 8} have the property we want to prove S has.