Consider the following infinite set A over = {a, b, c, d, e, g}.

Set A consists of pairs. The first member of each pair is an odd length string.

The second member of each pair is a character that shows the middle symbol of the first string.

If the middle symbol is a' b' then there are only a's to its left and there are only c's to its right.

If the middle symbol is a' e' then there are only ds to its left and there are only g's to its right.

The set is written in rows below for clarity of exposition.

A = { [b, b], [abc, b], [aabcc, b], . . . [e, e], [deg, e], [ddegg, e], . . . }

Give a recursive definition of the set A. Write all three components of the recursive definition including the closure (Basis, Recursive Step, Closure)