= Solution
The <prime numbers> $2,3,5$ form the lower <antichain>; the nonprime elements $1,4$ form the upper <antichain>. In particular, $1$ is not a <prime number>. Each lower element is below each upper element, and no third element can lie strictly between them. Therefore \b[the six <cover relations> are $2,3,5\prec1,4$], represented by the following <Hasse diagram>. Upward movement represents increasing order; crossing lines do not add elements.
\Image[/past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit-hasse.png]
{title=The six cover relations for the five-element partial order}
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