Question

Which of the following is an element

Answer 1

We can easily enumerate E and F:

$E = \{ 1,4,9 \}$

$F = \{ 2,4,6,8 \}$

The intersection $E \cap F$ is a set composed by all the element belonging to both E and F, i.e. 4.

The intersection of this set with D works in the same way, but it's actually a trivial one, since $E \cap F$ is a subset of D. In fact, D is the set of all integers, while 4 is a particular integer. And in general, if A is a subset of B, then the intersection between A and B is A itself, so the final answer is

$D \cap (E \cap F) = \{4\}$

Answer 2

Sets are a great way to make any question confusing.

We're interested in the intersection of all three sets. There's no need for the parentheses; intersection is associative.

An element in the intersection is an element in all three sets, so a whole number (doesn't rule out any choices), perfect square between 1 and 9 (rules out 3, 6 and 16 but 4 remains) and an even number between 2 and 9 (4 is in that one too).

Second choice: 4