Another way of solving this question can be like this:-
important point:- For a poset [Dn ; /] to be a boolean algebra the number of elements in the lattice should be of the form 2m.
D110 = { 1,2,5,10,11,22,55,110 } , none of the numbers is a perfect square and the number of elements in the lattice is 8=23. So , it is a boolean algebra.
D91 = { 1,7,13,91} none of the numbers is a perfect square so D91 is square free.And the number of elements in the lattice is 4 which is nothing but 22. So, it is a boolean algebra.
D45 = {1,3,5,9,15,45} 9 is a perfect square.Also the number of elements is not a power of 2.So, it is not a boolean algebra.
D64 = {1,2,4,8,16,32,64} It has got 3 perfect squares.Also the number of elements is 7 which is not of the form 2m. So it is not a boolean algebra.
I hope you got it...