Explanation:

- Statement 1: The Satavahana Kings were notable patrons of the Prakrit language. This language was extensively used in their inscriptions and literature, indicating their patronage and encouragement of Prakrit.

- Statement 2: The Satavahana period is marked by significant developments in public art, especially evident in architectural sites like the Amaravati Stupa and the Ajanta caves. This reflects their support and encouragement towards public artistic expressions.

- Option 1: Only 1

- This option claims only Statement 1 is true.

- Option 2: Both 1 and 2

- This option claims both statements are true, which aligns with historical evidence.

- Option 3: Only 2

- This implies only the public arts were encouraged which is partially accurate.

- Option 4: Neither 1 nor 2

- This dismisses the credit to the Satavahanas which is incorrect.

The Satavahana rulers indeed fostered the Prakrit language and public arts, so:

Option 2: Both 1 and 2 is correct.