1. Give an analytic verification of K n - k 2 + k(n - k)+ 2 Now give a combinatorial justification of this identity. 2. If P(E) = 0.8 and P(F)= 0.9 then show that P(EnF) 2 0.7 In general, show that, P(En F) _ P(E) +P(F)-1. 3. Let fn denote the number of ways of tossing a coin n times such that successive heads never appear. Argue that fn = fn-1+ fn-2 for n > 2, where fo = 1 and f1 = 2. Hint: How many outcomes are there that start with a head, and how many start with a tail