it is given that set with a relation Relation R which is transitive, antisymmetric and reflexive so it is already a poset .Additionally, it is guaranteeing about the existence of LUB and GLB too.so now it is : Poset + Having lub and Glb both , That is Lattice . so option A and C both r true .
For being option B true it needs some extra information that is :
A lattice can be Boolean Algebra only when It is distributed lattice , complimented lattice and bounded lattice along with it will have to satisfy the properties of Boolean algebra . and we dont have any such info about this lattice .
counter of B is :
it is poset, lattice but not B.A