Consider the following game tree. In this tree, a player, say Player $2,$ has an information set with three nodes, I, II$,$ and III in it$.$ Another player, say Player $3,$ has an information set with two nodes, IV and V$,$ in it$.$ Explain whether each of the following is true or false.$($a$)$ Node I is Player $3$s decision node.$($b$)$ Player $2$ has three actions at node III and two at node I.$($c$)$ Player $3$ has exactly two actions at node IV$,$ labeled as a$,$ b$,$ and two actions at node V$,$ labeled as b$,$ c$.($d$)$ The game is one of perfect information.$($e$)$ When she is called upon to move, Player $3$ cannot distinguish node IV from node V$.$