Actually, this qs is about to make COMPLETE Lattice.
If we add {a} then it becomes a complete lattice.
First of all draw the Poset diagram with {a}.And plz don't use the Shortcut for LUB of A and B = A U B and GLB of A and B =A∩B
Just see the Poset diagram and find out the LUB and GLB for every pair of elements.
Let eg1. subset A= {{1,2},{1,3,5}} then LUB of {1,2},{1,3,5} = {1,2,3,4,5} ∈ S and GLB of {1,2},{1,3,5} ={1} ∈ S
Let eg2.subset B={{1,2,3},{1,3,5}} then LUB of {1,2,3},{1,3,5} = {1,2,3,4,5} ∈ S and GLB of {1,2,3},{1,3,5} = {1}
The correct answer is ,(A) {1}