(5 pts) Let Diff  (of uncovered white squares) - (of uncovered black squares) in the initial modified board (i

(5 pts) Let Diff  (of uncovered white squares) - (of uncovered black squares) in the initial modified board (i.e., before any dominoes have been placed). Use induction to establish that the following invariant holds regardless of how many dominoes have been placed: Invariant: The difference between the number of uncovered white squares and the number of uncovered black squares, i.e., (# of uncovered white squares) - (# of uncovered black squares), is equal to Diff. Make sure to state explicitly what P(n) is. Hint: let Wi and Bi be the number of uncovered white and black squares, respectively, after i dominoes have been placed on the modified board.