Consider the set $\{2,3,4\}$ and define partial ordering if $a$ divides $b$. Element 3 is not related to anybody else therefore after Hasse Diagram element 3 is maximal or minimal.
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Yes, 3 is both minimal and maximal. 2 is minimal; 4 is maximal.
Exercise. What are the maximal chains and maximal antichains?
William Elliot
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