I have an assignment of determining whether this lattice is distributive and complemented or not. I was able to determine that the lattice is indeed complemented as I found at least one complement of every element of the lattice. I tried to determine whether it's distributive or not but I'm sure if I was correct.
The lattice is distributive if it doesn't contain any sub-lattice that's isomorphic to a pentagon or a diamond. I think that there's a sub-lattice (E, B, A, C, F) that's isomorphic to pentagon, so the lattice then wouldn't be in fact distributive, but I'm not sure about this.