2. Weak Induction (15 points) (1) (5 points) Using weak induction, prove that 36. 2) (5 points) Prove that log(n!) nlog(n) for all integers n21 Reminder 1: log(1)-0 Reminder 2: log(a b) log(a) log(b) Reminder 3: If a S b then log(a) log(b) Note: The base of the logarithms doesn't matter for any of the above. (3) (5 points) Prove for all integers n21 that if Ai, A2, . An and B are sets, then: Hint: Use the fact that (XnY)UZ-(XUz)n (YUZ) where X, Y, and Z are sets