Solution

Greedy best‐first search is not optimal but is often efficient: TRUE
Greedy best-first search tries to expand the node that is closest to the goal, that is, minimal h(n), on the grounds that this is likely to lead to a solution quickly. Hence, it is considered efficient but neither optimal nor complete.

A* is complete and optimal provided h(n) is admissible or consistent: TRUE
Provided heuristic meets some basic conditions, A* is both complete and optimal. A heuristic h(n) is admissible if for every node n, h(n) ≤ h*(n), where h*(n) is the true cost to reach the goal state from n. An admissible heuristic never overestimates the cost to reach the goal, that is, it is optimistic.

Recursive best‐first search is efficient in terms of time complexity but poor in terms of space complexity: FALSE
This statement is false because the inverse is true: Recursive best‐first search is not particularly efficient in terms of time complexity but is relatively good in terms of space complexity.

h(n) = 0 is an admissible heuristic for the 8‐puzzle: TRUE
h(n) = 0 is an admissible heuristic for the 8‐puzzle because h(n)=0 NEVER over-estimates the remaining optimal distance to a goal node. Non-admissible heuristic may overestimate the cost of reaching the goal.