Which of the following writs is a challenge to the legality of a prisoner's detention?

Habeas corpus

The correct answer is Option (3) → Habeas corpus

Out of the listed writs, the one that challenges the legality of a prisoner's detention is:

• Habeas Corpus

Here's a breakdown of the writs and their functions:

• Habeas Corpus: This writ literally translates to "you have the body" and is used to bring a prisoner before the court to determine the legality of their detention. If the court finds the detention unlawful, the prisoner may be released.
• Mandamus: This writ orders a public official or a lower court to perform a specific legal duty that they are neglecting or refusing to perform.
• Certiorari: This writ is used to order a lower court or tribunal to transfer a case to a higher court for review.
• Quo Warranto: This writ challenges the right of a person to hold a public office.