a. Prove that in an 8 ×8 checkerboard with alternating black and white squares, if the squares in the top right and bottom left corners are removed the remaining board 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 x 2n checkerboard with alternating 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.
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