a. Prove that in an 8 8 checkerboard with alternating black and white squares, if the squares in the top right andbottomleftcornersareremovedtheremainingboard cannot be covered with dominoes. (Hint: Mathematical induction is not needed for this proof.) b. Use mathematical induction to prove that for all integers n, if a 2n 2n checkerboard with alternat- ing black and white squares has one white square and one black square removed anywhere on the board, the remaining squares can be covered with dominoes.