Supervisory jurisdiction refers to the power of superior courts of general superintendence over all subordinate courts. Through supervisory jurisdiction, superior courts aim to keep subordinate courts within their prescribed sphere, and prevent usurpation. In order to exercising such control, the power is conferred on superior courts to issue the necessary and appropriate writs. Each court of appeal has supervisory jurisdiction, subject to the general supervisory jurisdiction of the Supreme Court, over all inferior courts in all cases in which an appeal would lie to the court of appeal. Therefore, not only the SC, but HCs also exercise this power over their subordinate courts. Hence, statement 1 is incorrect.
The Supreme Court can issue writs only for the purpose of enforcement of Fundamental Rights but not for any other purposes. The High Court, on the other hand, can issue writs not only for the purpose of enforcement of Fundamental Rights, but also for other purposes. Writ jurisdiction of the HC is wider than that of the SC.