question and answer

Hello

Im having trouble with problem #17 in section 4.4, the book gives a hint so i thought in the back so I thought to prove that R is reflexive, antisymmetric and transitive on A. Is there an another route that might not take as long or Im I going about it ok??

Thank you
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17.  If a subset of a partially ordered set has exactly one minimal element, must that element be a smallest element?  Give either a proof or a counter example to justify your answer.

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As you say, the back of the book gives a relation, a subset and a point in that subset that they claim is acounter example. The trick is to show that the relation is a partial order, and that the point and subset  have the needed properties.