Consider following sentences regarding A*, an informed search strategy in…

Summary: Statements (a) and (c) are true; statement (b) is false as written.

Definition: C* is the cost of an optimal solution path.

• Statement (a): A* expands all nodes with f(n) < C*.

  Explanation: With an admissible heuristic (one that never overestimates remaining cost), f(n) = g(n) + h(n) is a lower bound on the cost of any solution through n. Any node whose f-value is strictly less than the optimal cost must be expanded before an optimal goal can be found, so A* will expand all nodes with f(n) < C*.

• Statement (b): A* expands no nodes with f(n) = C*.

  Explanation: This claim is false as an absolute statement. A* is guaranteed not to expand nodes with f(n) > C* once the optimal solution cost is known, but nodes with f(n) = C* may or may not be expanded depending on tie-breaking rules and implementation details. Therefore you cannot assert that A* expands no nodes with f(n) = C* in all cases.

• Statement (c): Pruning is integral to A*.

  Explanation: In practice, efficient implementations of A* use pruning techniques such as maintaining a closed set (to avoid re-expanding already-seen states), discarding dominated paths, and other optimizations. While you can describe a bare A* tree search without some forms of pruning, pruning and duplicate-state handling are integral to making A* efficient and are standard in most descriptions of A* as used in practice.

Conclusion: The correct combination is that the first statement and the third statement are true, while the second statement is not generally true.