4. Show that a lattice L is a chain iff every nonempty subset of L is a sublattice. 5. Let L=P(S) be the lattice of all subsets of a set S under the relation of containment. Let T be a subset of S. Show that P(T)is a sublattice of L 6. Let L be a lattice and let a and b be element of L such that a s b. The interval a, b is defined as the set of all a E L such that a< a s b. Prove that [a, b] is a sublattice of L 7. Describe a practical method of checking associativity in a join-table and in a meet-table.4. Show that a lattice L is a chain iff every nonempty subset of L is a sublattice. 5. Let L = P(S) be the lattice of all subsets of a set S under the relation of containment. Let T be a subset of S. Show that P(T) is a sublattice of L. 6. Let L be a lattice and let a and b be element of L such that a ≤ b. The interval [a, b] is defined as the set of all x ∈ L such that a ≤ x ≤ b. Prove that [a, b] is a sublattice of L. 7. Describe a practical method of checking associativity in a join-table and in a meet-table. 7