MAT 243 Written Homework #6 5.3 Due: April 5 Solve the following problems, showing any necessary work. 1. [5 points) Let A be the set of binary strings defined recursively by a. 1, 1101 E A, b. if x E A, then xlxR, r101, 2RxzR e A, and c. every element of A can be obtained from (a) by applying (b) a finite number of times. Use Structural Induction to prove that every element of A has an odd number of 1's in it