1. Strings and Induction (1 page) Give a careful proof of the following proposition using proof by induction : For all i > 0, and all strings we , (WR)' = (w), where wR is the reverse of string w. Hint: It is a good idea to read section 2.1.2 of Rich before working on this problem. Use the definition of the reverse of a string given on page 9 of Rich. You may also use Theorem 2.1 on the bottom of page 9 of Rich in your proof