A lattice is a distributive lattice if each element has at most one complement.
Complements of b are c and d.
So, not distributive.
It sure is a lattice, though. So, Option B
Why is it not a Boolean algebra?
- If every element of the lattice has at least one complement => Complemented lattice.
- If every element of the lattice has strictly either 0 or 1 complement => Distributive lattice.
- A complemented distributed lattice is a necessary condition for being Boolean algebra. (So Option D is False)