Consider the following statements which one of them is incorrect?

Answer: 'None of these' is correct because all three statements are true.

• A finite lattice is always bounded — Reason: In a finite lattice the join of all elements (computed iteratively using pairwise joins) yields a greatest element and the meet of all elements yields a least element, so the lattice has both top and bottom.

• A bounded and complemented lattice may or may not be distributive — Reason: Complementation means each element has at least one complement, but distributivity is an independent, stronger property. For example, the five-element nondistributive lattice M3 is bounded and complemented but not distributive. A complemented distributive lattice is a Boolean algebra, but complemented alone does not imply distributivity.

• Complemented lattice is a proper subset of bounded lattice — Reason: By definition a complemented lattice is bounded and every element has a complement, so complemented lattices are contained in bounded lattices. The inclusion is proper because there exist bounded lattices that are not complemented; for example, the three-element chain 0 < a < 1 is bounded but the middle element a has no complement.

Therefore, none of the three given statements is incorrect; selecting 'None of these' is the correct answer.