Let U = {1, 2, 3, 4, 5, 6, 7}, with A = P(U), and let R

Question:

Let U = {1, 2, 3, 4, 5, 6, 7}, with A = P(U), and let R be the subset relation on A. For B = {{1}, {2}, {2, 3}} ⊆ A, determine each of the following.
(a) The number of upper bounds of B that contain
(i) Three elements of U;
(ii) Four elements of U;
(iii) Five elements of U
(b) The number of upper bounds that exist for B
(c) The lub for B
(d) The number of lower bounds that exist for B
(e) The glb for B