Mathematics
Mathematics, 07.04.2020 17:25, lflugo6oyn4sp

A subset T of the integers is defined recursively as follows: Base case: 2 ∈ T Recursive rule: if k ∈ T, then k + 5 ∈ T This problem asks you to prove that T is exactly the set of integers that can be expressed as 5m+2, where m is a non-negative integer. In other words, you will prove that x ∈ T if and only if x = 5m+2, for some non-negative integer m. The two directions of the "if and only if" are proven separately. (a) Use structural induction to prove that if k ∈ T, then k = 5m + 2, for some non-negative integer m.

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A subset T of the integers is defined recursively as follows: Base case: 2 ∈ T Recursive rule: if k...

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