Final answer:
The most likely disease associated with a dog presenting polyuria and polydipsia is diabetes mellitus, which is characterized by insulin problems and high blood glucose levels.
Step-by-step explanation:
A 9-year-old dog presenting with polyuria (frequent urination) and polydipsia (excessive thirst) would likely be associated with several diseases, but given the options, diabetes mellitus is the correct answer. Diabetes mellitus is a disease caused by problems with the pancreatic hormone insulin, leading to high blood glucose levels. Other symptoms can include polyphagia (increased hunger), weight loss, and lethargy. In animals, as in humans, diabetes can be caused by an autoimmune process when the immune system mistakenly attacks the pancreatic cells, leading to type 1 diabetes mellitus.