Final answer:
False advertising and violation of conduct rules are most likely to be considered violations of Article 6, based on the provided references.
Step-by-step explanation:
The student has asked which of the listed items are stated violations of Article 6. Referring to the provided references, gross negligence is not explicitly mentioned as a violation under Article 6, though it could potentially fall under broader categories of abuse of office or legal misconduct. False advertising is generally regarded as illegal, particularly when it constitutes fraud, and could be considered a violation of the law as per our reference. However, improper signage is not specifically cited as a violation of Article 6, but it may, in certain contexts, go against business expression regulations mentioned in the references.
Practicing nepotism, while often frowned upon, is not identified as a violation of Article 6 in the information provided. Incompetence may be related to the broader issues of abuse of office but is not clearly defined as a violation of Article 6. Lastly, a violation of conduct rules could certainly be encompassed by Article 6 if those rules are legally binding. Given the information, false advertising and violation of conduct rules are most clearly aligned with Article 6 violations.