State for each of the following statements whether it is true or false, by entering a T for the statements that are true and an F for the statements that are false. Please mention the statement number before each answer, so that answers can be related to the statements.

$(1)$ Some search strategies are neither complete nor optimal.

$(2)$ Some search strategies are complete and optimal under certain conditions.

$(3)$ A frontier contains nodes that are yet to be expanded.

$(4)$ Space complexity of depth$-$first search $($DFS$)$ is highest among blind searches.

$(5)$ Depth$-$first search may expand shallower nodes later.

$(6)$ A$*$ can be used only if an admissible heuristic is available.

$(7)$ Greedy Best$-$First Search expands node with lowest value of g first, where g$($n$)$ is the cost of the path from root to node n$.$

$(8)$ Outputs of a heuristic function are never goal$-$dependent.

$(9)$ A$*$ expands node with lowest value of h first, where h$($n$)$ is the value of the heuristic function for node n$.$

$(10)$ h$($n$),$ where h is a heuristic function, is an estimate of the cost of the most expensive path from node n to goal.