1. Prove that the equation (p/q)2 - 3 has no solution for p,q e N. 2. Prove that if x (a,b}* and abx - xab, then x - (ab)[n] for some n eN using contradiction. 3. Prove that if x (a,b}' and xba - bax, then x - (ba)[n] for some neN using contradiction. 4. Prove by mathematical induction that 't'i 1 = n(n + 1)/2. 5. Show that there are no strings x,y ybx using induction. Textbook Computability,Complexity, and Languages Author: Davis, Sigal, Weyuker Chapter 1 Exercise (a,b)" such that xay