Solution:

Habeas corpus is a recourse in law challenging the reasons or conditions of a person’s confinement under color of law.

Mandamus is a judicial remedy in the form of an order from a superior court, to any government subordinate court, corporation, or public authority, to do some specific act which that body is obliged under law to do (or refrain from doing).

Certiorari is issued by a superior court, directing an inferior court, tribunal, or other public authority to send the record of a proceeding for review.

Quo warranto is a prerogative writ requiring the person to whom it is directed to show what authority they have for exercising some right or power (or “franchise”) they claim to hold.