1. Compute 30 5i11 i=2 2. Find the sum 3 + 2 + 7 + 12 + . . . + 252 3. Use mathematical induction to show that for any positive integer n, 6 ever divides 7 -1. 4. Give a recursive definition of the set of all positive even integers 5. Give a recursive algorithm for finding the mode of a list of integers. (The me is the most frequently occurring number found in a set of numbers. You assume that the list of integers is already ordered in increasing order.) 6. For the following relation on the set (x, y, z, w, t) (a) Give its arrow diagram representation (b) Give its matrix representation (c) Is it reflexive? Explain why and why not (d) Is it symmetric? Explain why and why not. e) Is it anti-symmetric? Explain why and why not . ( (f) Is it transitive? Explain why and why not (g) Find R 7. Let R (1,2),(1,3), (1,4),(2.2),(2,3), (3,3),(3,4),(4,4)) and (1,2), (1,3), (2, 1), (2,3),(3,4)) be relations on set (1,2,3,4 R2 = { Find Ro o R