Final answer:
The statement that all unicellular organisms are prokaryotes is false; examples like Paramecium, which are eukaryotic, demonstrate that there are also single-celled eukaryotes. Furthermore, prokaryotes, which were the first to evolve, do not have a membrane-bound nucleus, unlike eukaryotes.
Step-by-step explanation:
The statement that all unicellular organisms are prokaryotes is false. While it is true that prokaryotic cells do not have a membrane-bound nucleus or other membrane-bound organelles like mitochondria, and all bacteria and archaea are prokaryotes, not all single-celled organisms fall into this category. Even though prokaryotic cells do not have mitochondria, they do have DNA, which is not contained within a defined nucleus.
Paramecium, which is a unicellular organism observed under a microscope, provides evidence that not all unicellular organisms are prokaryotes because it is a type of protist, and hence a eukaryote. Eukaryotic cells have a membrane-bound nucleus and other organelles, characteristics that are evident in the structure of Paramecium.
The first organisms to evolve were the prokaryotes. Prokaryotic cells are simpler and smaller in structure compared to eukaryotic cells, which fits with the theory of evolution that simple life forms evolved first, and more complex organisms evolved later.