Question: Let (A,R) and (B,S) be two partially ordered sets. We define on the product AB a relation T by: (a,b)T(c,d) if and only if (aRc)

Let (A,R) and (B,S) be two partially ordered sets. We define on the product AB a relation T by: (a,b)T(c,d) if and only if (aRc) and bSd. Prove that T is an order relation. Is AB totally ordered if A and B are? Justify your answer with a detailed proof, or with a counterexample and explanations

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