[Solved]Consider Following Recursive Definition Set X 1 12 X 2 15 X 3 X Y X X Y X 4 X Y X X Y X Pr Q37247486

Consider the following recursive definition of a set X.

1. 12 ∈ X

2. 15 ∈ X

3.  if x, y ∈ X, then x + y ∈ X

4. if x, y ∈ X, then x − y ∈ X

(a) Prove the following claim: Claim. Every member of X isdivisible by 3. Hint: You’ll want to do structural recursion on thedefinition of X, so there will be two base cases and two inductioncases.

(b) Prove the following claim: Claim. For every natural numbern, 3n ∈ X. Hint: In this case, you are not inducting on X, butinstead, you are inducting on the natural numbers.

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Answer to Consider the following recursive definition of a set X. 1. 12 ∈ X 2. 15 ∈ X 3. if x, y ∈ X, then x + y ∈ X 4. if… . . .