Let U = {1, 2, 3}. Let 2ᵁ denote the powerset of U. Consider an undirected…

Let U = {1, 2, 3}. Let 2ᵁ denote the powerset of U. Consider an undirected graph G whose vertex set is 2ᵁ.

For any A, B ∈ 2ᵁ, (A, B) is an edge in G if and only if (i) A ≠ B, and (ii) either A ⊆ B or B ⊆ A.

For any vertex A in G, the set of all possible orderings in which the vertices of G can be visited in a Breadth First Search (BFS) starting from A is denoted by ℬ(A).

If ∅ denotes the empty set, then the cardinality of ℬ(∅) is ________.