Which of the following statements is/are correct in a Bayesian network?

The state graph shows the action cost along the edges and the heuristic function $h$ associated with each state.

Suppose A* algorithm is applied on this state graph using priority queue to store the frontier. In what sequence are the nodes expanded?

Consider a hash table of size 10 with indices $\{0,1, \ldots, 9\}$, with the hash function

$$ h(x)=3 x(\bmod 10) $$

where linear probing is used to handle collisions. The hash table is initially empty and then the following sequence of keys is inserted into the hash table: 1 , $4,5,6,14,15$. The indices where the keys 14 and 15 are stored are, respectively

If a relational decomposition is not dependency-preserving, which one of the following relational operators will be executed more frequently in order to maintain the dependencies?