True or False. Please answer if the following statements are true $($T$)$ or false $($F$).$ If your answer is False, give a short meaningful explanation or counterexample. If your answer is True, prove it$.2$ pts for True or False. $3$ pts for short answer.

Consider a finite, acyclic search space where depth$-$first search is guaranteed to eventually find a solution and the root is not a goal. In this situation iterative deepening search will always explore more nodes than depth$-$first.