A) Give a recursive definition of the set of nonnegative integers that are multiples of 7. b) Give a recursive definition of the set of bit strings of even length that start with 0.

a)Let a be 7.Basic step: a ∈  S and a>=0. Recursive Step: a*7i ∈ S where i<=n, and S is the required set

b)Let λ be the empty string. Basis Step: λ ∈ S. Recursive Step: b ∈ S =⇒ 00b ∈ S & 01b ∈ S, and S is the required set  

Explanation:

Please check the answer section.

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