Which writ is issued by a court when it finds that a particular public office holder is not performing a legal duty and is thereby infringing upon the right of an individual?

Introduction / Context:
In constitutional law, especially in India, higher courts like the Supreme Court and High Courts have the power to issue various types of writs to protect fundamental rights and ensure that public authorities act within the law. This question focuses on identifying the correct writ that is used when a public official or authority fails to perform a mandatory legal duty, resulting in a violation of someone's rights.

Given Data / Assumptions:

• A court has determined that a public office holder is not performing a legal duty.
• This failure is infringing the right of an individual.
• The question refers to one of the traditional writs like Habeas Corpus, Mandamus, Prohibition and Quo warranto.
• We assume the context of Indian constitutional practice, where these writs are commonly discussed.

Concept / Approach:
The writ of Mandamus literally means "we command". It is issued by a court to a public authority, including a public office holder, directing them to perform a legal duty that they are bound to perform but have failed or refused to carry out. Habeas Corpus deals with illegal detention, Prohibition is issued to lower courts or tribunals to stop them from exceeding jurisdiction, and Quo warranto is issued to question the authority by which a person holds a public office. Therefore, when a legal duty is not performed and rights are affected, Mandamus is the appropriate writ.

Step-by-Step Solution:
Step 1: Identify from the question that a legal duty exists and is not being performed by a public official. Step 2: Recall the purpose of the writ of Mandamus: compelling performance of public duties by authorities. Step 3: Distinguish Mandamus from other writs by matching its function with the situation described. Step 4: Select Mandamus as the correct writ for enforcing performance of a legal duty.

Verification / Alternative check:
You can cross check by remembering typical examples: If a public authority is required by law to issue a licence, grant a benefit or consider an application, but fails to do so without justification, a court may issue Mandamus directing the authority to act according to law. This is different from ordering release from custody (Habeas Corpus), preventing a lower court from acting beyond jurisdiction (Prohibition), or questioning the legitimacy of a person holding office (Quo warranto). This comparison confirms that Mandamus fits the situation in the question.

Why Other Options Are Wrong:
Habeas Corpus: This writ protects personal liberty against illegal detention and is used to secure the release of a person unlawfully detained, not to compel performance of general public duties.
Prohibition: This writ is directed at lower courts or quasi judicial bodies to prevent them from exceeding their jurisdiction. It does not address failure to perform administrative duties.
Quo warranto: This writ is used to challenge the legality of a person's claim to a public office, asking "by what authority" they hold that office. It is not used to force them to perform a particular duty.

Common Pitfalls:
Students sometimes mix up Mandamus with Quo warranto because both relate to public offices. The key difference is that Mandamus compels performance of a duty, while Quo warranto questions the right to hold the office at all. Another pitfall is to pick Habeas Corpus for any rights violation, forgetting that it is specific to unlawful detention. Keeping the distinct purposes of each writ clear helps in answering such questions correctly.

Final Answer:
The writ used in this situation is Mandamus, which commands a public authority to perform its legal duty.