The two correct statements that describe cyanobacteria are:
- Cyanobacteria lived in the ocean.
- Cyanobacteria were the first photosynthesizing organism.
Cyanobacteria are photosynthetic prokaryotes found in various environments, including oceans, and they played a crucial role in the oxygenation of the Earth's atmosphere through their photosynthetic activities. They do not contain a nucleus, as they are prokaryotic organisms.