* 1.4 The strings of balanced parentheses can be defined in at least two ways. 1) A string w over alphabet {C} is balanced if and only if: a) w has an equal number of ('s and y's, and b) any prefix of w has at least as many 's as )'s. 2) a) e is balanced. b) If w is a balanced string, then (w) is balanced. c) If w and x are balanced strings, then so is wx. d) Nothing else is a balanced string. Prove by induction on the length of a string that definitions (1) and (2) define the same class of strings