please answer question 8.

6 Functions 8 Let S be the set of all finite non-null strings of characters. Let upr:SS be the function that converts all lower-case letters to upper-case (and leaves all other characters unchanged) Similarly, let her: S S be the function that converts all upper- case letters to lower-case. (a) Evaluate upr('Barbara HillP) and (lwr oupr)('Barbara Hill') (b) Are upr and lwr inverses of each other? Explain. Let X (1, 2, 3, .., 20), and let Y be the set of non-null strings of up to 20 characters. Let fbe defined as follows: f:X Y, f(x) English word for x (in lower-case letters) For example, f( 1 )-'one (a) State, giving reasons, whether (i) fis one-to-one