Q4: (6 marks) We have seen that the Fibonacci numbers Fr count many different combinatorial objects. For example, Fn+1 is the number of ways to tile an n-board with monomers and dimers. (a) Use a bijection with monomer-dimer tilings to show that the number of subsets of {1, 2, . . ., n} with no consecutive numbers (including the empty set) is Fn+2. (b) Use your answer to (a) to show that the number of subsets of {1, 2, ..., n} with no consecutive numbers (including the empty set), where we also regard n and 1 as consecutive, is Fn-1+ Fn+1