Explanation:

- On 9th January 2020, the Legislative Assembly of a state in India adopted a new logo.

- The options given are:

- Option 1: Tripura

- Tripura is a state in northeastern India. However, it did not adopt a new legislative assembly logo on this date.

- Option 2: Assam

- Assam is also a northeastern state. Similarly, it did not introduce a new assembly logo on the specified date.

- Option 3: Andhra Pradesh

- Andhra Pradesh, located in the southern part of India, was not the state that adopted a new logo in January 2020.

- Option 4: Arunachal Pradesh

- Arunachal Pradesh, a state in the northeastern part of India, is indeed the state whose Legislative Assembly adopted a new logo on 9th January 2020.

- The logo's design incorporates significant symbols like the national emblem and state flower, showcasing the region's cultural heritage.