Consider a two player game in which player $1$ can choose A or B$.$ The game ends $($with payoff $(2,0))$ if he chooses A while it continues to player $2$ if he chooses B$.$ Player $2$ can then choose C or D$,$ with he game ending $($with payoff $(3,1))$ after C and continuing again with player $1$ after D$.$ Player $1$ then can choose E or F $,$ and the game ends $($with payoff $(0,0)$ and $(1,2)$ respectively$)$ after each of these choices.

$($a$)$ Represent this game in extensive form $($draw the game tree only$).(1$ point$)($b$)$ How many terminal nodes does the game have?$(1$ points$)$

$($c$)$ How many pure strategies does each player have? $(2$ points$)$

$($d$)$ Find a sub$-$game perfect equilibrium of this game? $(2$ points$)$

$($d$)$ Find a Nash equilibrium of this game which is not a sub$-$game perfect equilibrium? $(2$ points$)$