Consider the grammar:

(1) S i C t S

(2) S i C t S e S

(3) S a

(4) C b

where i, t, and, e stand for if, then, and else, and C and S for "conditional" and "statement."

(a) Construct a rightmost derivation for the sentence w = i b t i b t a e a.

(b) Show the corresponding parse tree for the above sentence.

(c) Is the above grammar ambiguous? If so, prove it.