An organic compound P of molecular formula ${\text{C}}_{\text{5}}{\text{H}}_{\text{8}}$ , when treated with Na in liquid  ${\text{NH}}_3$ followed by reaction with n – propyl iodide yields$\text{Q}\left({\text{C}}_{\text{8}}{\text{H}}_{\text{14}}\right)$ . P gives a ketone ${\text{R\hspace{0.17em}C}}_{\text{5}}{\text{H}}_{\text{10}}\text{O}$  , when treated  with dilute${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{\text{\hspace{0.17em}and\hspace{0.17em}HgSO}}_{\text{4}}$ . Q on oxidation with alkaline ${\text{KMnO}}_4$  gives two isomeric acids S and T of formula ${\text{C}}_{\text{4}}{\text{H}}_{\text{8}}{\text{O}}_{\text{2}}$ . The correct statement(s) among the following regarding this reaction

sequence is/are