Prove that for n odd an ntimesn chessboard missing its

Question

1. Compare the result of this truth table to your original idea. If they agree, explain how they are compatible. If they do not agree, find the source of the error.

2. If you have some time left over, work on these proofs.

(a) For n ∈ N, prove that if n³ +6n² -2n is even, then n is even.

(b) Let x ∈ R. Show that if x⁵ +7x³ +5x ≥ x⁴ +x² +8, then x ≥ 0.

(c) Prove that an 8× 8 chessboard with a square missing cannot be tiled with dominoes.

(d) Prove that for n odd, an n×n chessboard missing its lower-right-hand corner can be tiled with dominoes.