# 1) Given sets A and B as A= (0, 1, 2), and B=(a,b), (i) Write all the elements of powerset 2A (ii) Write all the elements of the Cartesian product A x B. #2) Prove by induction: For all! Integers n 21, the integer 5"-1 is divisible by 4. # 3) Prove by counter example: If a sum of two integers is even, then one of the summands is even. # 4) Prove by contradiction: if 3n+ 2 is an odd integer, then n is odd (Hint: odd integer is represented as 2k+1 where k is an integer)