I know what the definitions of maximal and minimal elements are but I'm not sure how to apply them in this case. Any help would be great.
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If you draw a picture of this partial order, you get this:
The only element with a strictly smaller element is $c$, so $c$ is the only non-minimal element; $a$ and $b$ are minimal, because there is no element strictly smaller than either of them.
Can you tell now what the maximal elements are?