Exercise 2.4 (40 pts) Based on the recursive definition of string and string concatenation ., use structural induction on the structure of strings to verify the following cancellation properties that for all strings x, y, z ( E*, (i) (10 pts) If x . y = x, then y = E. (ii) (10pts) If x . y = y, then x = E. (iii) (10 pts) If x . z = y . z, then x = y. (iv) (10pts) If x . y = x . z, then y = z