An ordering on a set A

Question

Let $A= \{2,3,4,5,6,7,8,9,10\}$.
An ordering on A is defined $x\leq y $ $\Leftrightarrow$ $y \; \text{is multiple of} \;x$.

Find the maximal and minimal elements of A. $2$ is the minimum or not ? $5$ is a maximal element ? I don't have any idea for this question.

Thanks your helping.

Answer 1

The minimal elements of $A$ are those which do not have any divisors in $A$: by inspection these are $2,3,5,$ and $7$.

The maximal elements of $A$ are those which do not divide any other elements of $A$: by inspection these are $7,8,9,$ and $10$.