6. A T-omino is a tile pictured below. Prove that every 2^n x 2^n (n > 1) chessboard can be tiled with T-ominoes. Let P(n) be the statement that every 2^n x 2^n (n > 1) chessboard can be tiled with T-ominoes. Basis Step. Verify the base case by providing an illustration. Next state the Inductive Hypothesis and continue on to complete the proof.
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In this case, we have a 4x4 chessboard. We can tile this chessboard with T-ominoes as follows: ``` TT TT TT TT ``` So, P(2) is true. Inductive Hypothesis: Assume that P(k) is true for some integer k > 1, i.e., every 2k x 2k chessboard can be tiled with Show more…
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