Solution\ (c) Let

S

be the set of all strings from

A^(**)

in which there is no

b

before an

a

. For example, the strings

\\\\lambda ,aa,bbb

, and

aabbbb

all belong to

S

, but

aabab!inS

. 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

xinA^(**)

, let bCount

(x)

be the number of occurrences of the character

b

in

x

. Give a recursive definition for bCount.\ Feedback?

(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 xA, let bCount (x) be the number of occurrences of the character b in x. Give a recursive definition for bCount