Policy Function and Value Function

$1$ point possible $($graded$)$

From the following options select one or more statement$($s$)$ which are true about the optimal policy function ${}^{*}$

$,$ the optimal value function $V^{*}$ and the optimal $Q-$function $Q^{*}$

${}^{*}(s)$ records the action that would lead to the best expected utility starting from the state $s$

${}^{*}(s)$ records the action that would necessarily lead to the best immediate reward for the current step

$V^{*}(s)=ma{x}_a{Q}^{*}(s,a)$ holds for all states $s$

$V^{*}(s)=ma{x}_a[{\displaystyle \underset{s^{\text{'}}}{\overset{?}{}}}T(s,a,s^{\text{'}})(R(s,a,s^{\text{'}})+V^{*}(s^{\text{'}}))]$ must hold true for the optimal value

function when