List all maximal and minimal elements of the partial order R = {(a,a), (b,b), (c,c), (a,c)}

Question

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.

Answer 1

If you draw a picture of this partial order, you get this:

            c  
            |  
            |     b  
            |  
            a

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?