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.