Question

Which is not true of romanticism? appeals to the imagination and emotion emphasis on symbolism and meaning tone is either dark and Gothic or exuberant, but always sincere it must be believable; there are no elements of the fantastic or supernatural

Answer 1

The answer which is not true of romanticism is that it must be believable; there are no elements of the fantastic or supernatural. 
As a matter of fact, there often are. Take Edgar Allan Poe, for example, who was a romanticist, and loved writing about the supernatural. 

Answer 2

Romanticism refers to a time in history when emotions were encouraged. Out of the list you have. Elements that are included are:
1. Appeals to the imagination - Correct
2. Emotional emphasis on symbolism and meaning- Correct
3. Tone is either dark and Gothic or exuberant, but always sincere. It must be believable - Incorrect. Anything should be possibly. Consider Romanticism like a magical land of wonders where if you believe it, it will be possible.
4. There are no elements of the fantastic or the supernatural - again incorrect as explained in number 3.