# Discrete Math Question

Let A = {a, b}(a)Give a recursive definition for A*.(b)The set A+ is the set of strings over the alphabet {a, b} of length at least 1. That is A+ = A* – {?}. Give a recursive definition for A+.(c)Let S be the set of all strings from A* in which there is no b before an a. For example, the strings ?, aa, bbb, and aabbbb 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.)(d)For x ? A*, let bCount(x) be the number of occurrences of the character b in x. Give a recursive definition for bCount.

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