1.7.2. Prove each of the following using the inductive definition of reversal given in the text.

(a) Prove, using the definition of concatenation given in the text, that concatenation of strings is associative. (b) Give an inductive definition of the concatenation of strings. (c) Using the inductive definition from (b), prove that the concatenation of strings is associative. Prove each of the following using the inductive definition of reversal given in the text. (a) (w^R)^R = w for any string w. (b) If v is a substring of w, then v^R is a substring of w^R. (c) (w^i)^R = (w^R)^i for any string w and i greaterthanorequalto 0