A TOS on n elements is BA iff n=2. So, Option D is false.
In a distributive lattice each element has atmost one complement (that is either no complements or 1 complement.
In a lattice if upper bound and lower bound exists then it is called a bounded lattice. Let L be a bounded lattice, if each element of L has complement in L , then L is called a complemented lattice. In a complemented lattice each element has atleast one complement. A lattice is boolean algebra if it is both distributive and complemented. So in a boolean algebra each element will have exactly one complement.
The hasse diagram is identical to hasse diagram for the poset So its a boolean algebra. Complement of 10 is 11, Complement of 110 is 1, Complement of 22 is 5, Complement of 55 is 2, And vice - versa.
Every total ordered relation is distributive but a total order relation which contain more than 2 elements cant be complemented since in a total ordered chain elements are directly related , so we wont get complements for elements other than Upper bound and lower bound.
Option D is the correct answer