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Suppose R is a partial order on A and S is a partial order on B. Define a relation T on A B such that

  • Suppose R is a partial order on A and S is a partial order on B. Define a relation T on A B such that (a1, b1) T (a2, b2) iff a1 R a2 and b1 S b2. Is T a partial order on A x B? Either provide a proof to show that this is true or provide a counterexample to show that this is false.

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