A partially ordered set is a bounded lattice if and only if every finite set of elements (including the empty set) has a join and a meet. For every element x of a poset it is trivially true (it is a vacuous truth) that a : x a (\displaystyle
orall a\in arnothing :x\leq a) and a : a x (\displaystyle
orall a\in arnothing :a\leq x) , and therefore every element of a poset is both an upper bound and a lower bound of the empty set. This implies that the join of an empty set is the least element = 0 (\displaystyle igvee arnothing =0) , and the meet of the empty set is the greatest element = 1 (\displaystyle igwedge arnothing =1) . This is consistent with the associativity and commutativity of meet and join: the join of a union of finite sets is equal to the join of the joins of the sets, and dually, the meet of a union of finite sets is equal to the meet of the meets of the sets, i.e., for finite subsets A and B of a poset L,

Can we conclude that does the system of all subsets of a finite set under the operation subset of form a lattice?
no