To determine the appropriate diagram showing the relationship between the categories FOOD, VEGETABLES, ROOTS, and ICECREAMS, we need to understand the classification:

• FOOD: This is the largest category and includes all types of edibles such as Vegetables, Roots, Icecreams, etc.
• VEGETABLES: This is a subset of FOOD, which includes all types of vegetables. Some vegetables can be roots, but not all.
• ROOTS: These are a type of Vegetables that grow underground, such as carrots and potatoes.
• ICECREAMS: These are a type of FOOD but are not related to Vegetables or Roots.

Now, let's examine the options:

• Option A shows overlapping circles that do not clearly separate the categories.
• Option B suggests some overlap between the categories that does not accurately reflect the relationship.
• Option C: There is a large circle representing FOOD. Inside FOOD, there is a separate circle for ICECREAMS. There is another circle for VEGETABLES, which contains a smaller circle for ROOTS. This accurately reflects the subset relationships.
• Option D fails to correctly show the subset relationships between the categories.

Therefore, the correct diagram is shown in Option C, illustrating that VEGETABLES are a subset of FOOD, ROOTS are a subset of VEGETABLES, and ICECREAMS are a separate part of FOOD.