Find grammars for that generate the sets of

(a) all strings with exactly two a's.

(b) all strings with at least two a's.

(c) all strings with no more than three a's.

(d) all strings with at least three a's.

(e) all strings that start with a and end with b.

(f) all strings with an even number of b's.

In each case, give convincing arguments that the grammar you give does indeed generate the indicated language.

= {, }