Final answer:
The true statement based on the sets given is option b: (E ∩ F) is the empty set, as there are no elements that belong to both sets E and F.
Step-by-step explanation:
The correct answer is option b. D ∩ (E ∪ F) represents the set of whole numbers that are either a perfect square less than 36 or an even number between 20 and 30. Considering set E, we have perfect squares less than 36, which are 1, 4, 9, 16, and 25. Set F is the set of even numbers between 20 and 30, which are 22, 24, 26, and 28. Combining sets E and F, we have {1, 4, 9, 16, 25, 22, 24, 26, 28}.
Now we must find the intersection with set D, which includes all whole numbers, thus just retaining those already in (E ∪ F). The intersection, therefore, will only include those values that are both whole numbers and elements of the combined set (E ∪ F), so it cannot be all whole numbers as option a suggests. It is not 16 or 25 specifically because the intersection includes multiple numbers that fit the criteria, not just a single value. Finally, the statement b seems the most accurate as none of the numbers in F are perfect squares, hence (E ∩ F) must be the empty set.