a. $A∗$ expands all nodes with $f(n)<C∗$ - This statement is true. $A∗$ expands nodes based on the total estimated cost $(f(n))$, and it prioritizes nodes with lower costs. $C∗$ represents the cost of the optimal solution path.
b. $A∗$ expands no nodes with $f(n)>C∗$ - This statement is false. $A∗$ uses an admissible heuristic, and nodes with estimated costs $(f(n))$ higher than the cost of the optimal solution $(C*)$
) are not expanded.
c. Pruning is integral to $A∗$ - This statement is true. $A∗$ employs pruning to avoid exploring paths that are guaranteed to be suboptimal. This is achieved through the use of heuristics that guide the search process efficiently.
So, the correct answer is:
B. Both statements a and statement c are true