To find the false statement, we first need to combine the given premises to understand the definite relationships between the four categories: apples, blackberries, doughnuts, and coconuts.

1. Blackberries and Doughnuts are Mutually Exclusive: We are given that "All blackberries are coconuts" and "No coconut is a doughnut." From this, we can make a certain deduction: no blackberry can possibly be a doughnut, as the entire blackberry category is inside a category that is completely separate from doughnuts.
2. Apples and Coconuts Overlap: We know "Some apples are blackberries." Since all blackberries are also coconuts, it logically follows that these specific apples must also be coconuts. Therefore, we can deduce that some apples are coconuts.

Evaluating the Statements

Now we can test which of the four options is false based on our deductions.

• A. "Some blackberries are doughnuts."
  This is False. As established in our first point, the blackberry and doughnut categories cannot overlap.
• B. "Some coconuts are apples."
  This is True. As established in our second point, the premises guarantee an overlap between coconuts and apples.
• C. "All coconuts are not apples."
  This statement is interpreted as "It is not true that *all* coconuts are apples," which is True. (We only know *some* coconuts are apples, not all of them).
• D. "All doughnuts are not coconuts."
  This is True. It is a direct restatement of the premise "No coconut is a doughnut."

Final Answer: Statement A is the only one that is unambiguously and logically false based on the premises.