Let S be the set of all strings from A* in which there is no b before an a. For example, the strings λ, aa, bbb, and aa all belong to S, but aabab ∉ S. Give a recursive definition for the set S. (Hint: a recursive rule can concatenate characters at the beginning or the end of a string.)

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Explanation:

A recurvsive defintion for which contains all possible strings over the alphabet is \lambda\in (contains the null strings) and

A recurvsive defintion for which contains all possible strings over the alphabet is (contains the strings of lengths 1) and

and

is the required recursive definition for S

For example, also

Again, as and from

And as from we have

i think the answer is b.