Determine the correct $(T)$ and incorrect $(F)$ statements from the following:
$(a)$ The $E^o$ for $MnO_4^- + 8H^+ + 5e^- \to Mn^{2+} + 4H_2O$ is $-1.52 \ V$.
$(b)$ $MnO_4^-$ oxidizes $I^-$ to $I_2$.
$(c)$ The color of $CrO_4^{2-}$ is yellow in the presence of $H^+$.
$(d)$ The color of $CrO_4^{2-}$ is yellow in the presence of $OH^-$.

(B) The standard reduction potential for the reaction $MnO_4^- + 8H^+ + 5e^- \to Mn^{2+} + 4H_2O$ is $+1.51 \ V$,not $-1.52 \ V$. Thus,statement $(a)$ is $(F)$.
$(b)$ $MnO_4^-$ is a strong oxidizing agent and it oxidizes iodide ions $(I^-)$ to iodine $(I_2)$. Thus,statement $(b)$ is $(T)$.
$(c)$ In acidic medium $(H^+)$,$CrO_4^{2-}$ (yellow) converts to $Cr_2O_7^{2-}$ (orange). Thus,statement $(c)$ is $(F)$.
$(d)$ In basic medium $(OH^-)$,the equilibrium shifts towards $CrO_4^{2-}$,which is yellow. Thus,statement $(d)$ is $(T)$.