Another easier way of solving is:=

Find out the greatest and least element, Here it is a and f respectively

For complements, check if the LUB and GLB of any 2 elements (here e with all the other elements) coincide with the greatest and least element respectively.

Here, **(e,c)(e,g)(e,d)** satisfies the above condition i.e. the LUB and GLB coincide with the greatest and least elements for all the 3 pairs.

But for (e,f), The upper bounds are a,b,e, and the **LUB is e. **But **LUB != maximal element**, so it is not a complement.