Upon reconsidering the provided options and the conditions for exclusion restrictions, it appears that the correct choice should indeed align with the given exclusion restrictions. Lets evaluate it again:The correct exclusion restrictions for an instrumental variable $($IV$)$ are:$1.$Relevance: The instrument Z must be correlated with the endogenous explanatory variable$\mathrm{.}2.$Exogeneity: The instrument Z must be uncorrelated with the error term in the regression.Based on the given conditions:$($i$)$ Z is correlated with the endogenous variable: True $($Relevance condition$)($ii$)$ Z is uncorrelated with the error term: True $($Exogeneity condition$)($iii$)$ Z does not appear in the regression: Not necessarily true $($The instrument Z can appear in the first stage of $2$SLS$)$