Which among the following statement(s) is(are) FALSE? A. Greedy best‐first…

Answer: Only the statement that claims recursive best-first search is efficient in time but poor in space is false.

• Greedy best-first search is not optimal but is often efficient: True. It uses a heuristic to select the node that appears closest to the goal, which can be fast in practice but does not guarantee an optimal path.

• A* is complete and optimal provided the heuristic is admissible or consistent: True. With an admissible heuristic A* never overestimates true costs and thus finds an optimal solution; consistency ensures nondecreasing f-values and guarantees optimality and completeness under usual assumptions.

• The claim that recursive best-first search is efficient in time but poor in space: False. Recursive best-first search (RBFS) is designed to be space-efficient, using linear space by avoiding storage of the full frontier. However, this memory savings can come at the cost of extra time due to repeated exploration, so the statement reverses the typical trade-off.

• h(n) = 0 is an admissible heuristic for the 8-puzzle: True. The zero heuristic never overestimates the true cost to the goal, so it is admissible (it reduces A* to uniform-cost/search).

Therefore, only the statement about recursive best-first search is false.