The answers to exercises marked [BB] can be found in the Back of the Book.
(a) Let A = Z2 and, for a = (a1, a2) and b = (b1, b2) in A, define a ≤ b if and only if a\ ≤ b\ and a1 + a2 ≤ b1 + b2. Prove that ≤ is a partial order on A. is this partial order a total order? Justify your answer with a proof or a counterexample.
(b) Generalize the result of part (a) by defining a partial order on the set Z" of n-tuples of integers. (No proof is required.)
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