The hydrocarbon A, adds one mole of hydrogen in the presence of a platinum catalyst to form n-hexane . When A is oxidised vigorouslty with `KMnO_4` , a single carboxylic acid, containing three carbon atoms , is isolated. Give the structure of A and explain.

A hydrocarbon (X) discharges the colour of cold alkaline KMnO_4 solution and reacts with warm dilute sulphuric acid containing HgSO_4 to form another compound (Y). (Y) gives positive iodoform test but does not react with Tollens' reagent. (Y), when distilled with 80% H_2SO_4 , gives sym-trimethylbenzene. Identify the compounds (X) and (Y) and write the reactions involved with proper reasons.

A compound [A] with molecular formula C_(5)H_(10)O gave a positive 2,4 -D.N.P. Test but a negtive Tollen's test. It was oxidised to carboxylic acid [B] with molecular formula C_(3)H_(6)O_(2) when treated with alkaline KMnO_(4) under vigorous conditions. Sodium salt of [B] gave a hydrocarbon [C] on Kolbe's electrolyte reaction. Identify [A],[B] and [C] and write the chemical equations for the reactions.