Discrete mathematics:

a. Use mathematical induction to prove that any checker-board with dimensions 3 x 2n can be completely covered with L-shaped trominoes for any integer n > 1. Hint: For the inductive step, note that a 3 x (2k + 2) checker-board can be split into a 3 x 2k checkerboard and a 3 x 2 checkerboard. b. Let n be any integer greater than or equal to 1. Use the result of part (a) to prove by mathematical induction that for all positive integers m, any checkerboard with dimen-sions 2m x 3n can be completely covered with L-shaped trominoes