Final answer:
The false statement about protists is that most protist cells have both mitochondria and chloroplasts. Not all protists have chloroplasts since only plant-like protists photosynthesize.
Step-by-step explanation:
The statement about protists that is NOT true in the subject of Biology is: 'Most protist cells have mitochondria and chloroplasts.' While it is correct that protist cells have a nucleus and can be parasites, and many protists do prefer water-based environments or are aquatic, not all protist cells contain both mitochondria and chloroplasts. Plant-like protists, such as algae, do contain chloroplasts for photosynthesis, but this is not the case for all protists. Animal-like and fungi-like protists might not contain chloroplasts as they do not all rely on photosynthesis for their food.