Algorithm

Let U = \{1, 2, 3\}. Let 2^U denote the powerset of U. Consider an undirected graph G whose vertex set is 2^U. For any A,B \in 2^U, (A,B) is an edge in G if and only if (i) A \neq B, and (ii) either A \subseteq B or B \subseteq 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 \phi denotes the empty set, then the cardinality of B(\phi ) is ____.

Consider functions Function 1 and Function 2 expressed in pseudocode as follows:

Let f_1(n) and f_2(n) denote the number of times the statement "x = x + 1" is executed in Function 1 and Function 2, respectively.
Which of the following statements is/are TRUE?

Let f and g be functions of natural numbers given by f(n)=n and g(n)=n^2.
Which of the following statements is/are TRUE?

Let G(V, E) be a directed graph, where V = \{1, 2, 3, 4, 5 \} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A.
A[i][j]= \left \{ \begin{matrix} 1 &1 \leq j \leq i \leq 5 \\ 0& otherwise \end{matrix} \right.
A[i][j]=1 indicates a directed edge from node i to node j . A directed spanning tree of G , rooted at r \in V , is defined as a subgraph T of G such that the undirected version of T is a tree, and T contains a directed path from r to every other vertex in V . The number of such directed spanning trees rooted at vertex 5 is ____

Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of G is/are TRUE?
MSQ