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 (a 1 , b 1 ) T (a 2 , b 2 ) iff a 1 R a 2 and b 1 S b 2 Is T a partial order on A x B Either provide a proof to show that this is true or provide a counter example to show that this is false ...

Given thatR is partial order on A and S is a partial order on B So exists Let sin ...

Suppose R is a partial order on A and S is a partial order on B. Define

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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 (a ₁, b ₁) T (a ₂, b ₂) iff a ₁ R a ₂ and b ₁ S b ₂. Is T a partial order on A x B? Either provide a proof to show that this is true or provide a counter example to show that this is false.