Respuesta :

We can easily enumerate E and F:


[tex] E = \{ 1,4,9 \} [/tex]


[tex] F = \{ 2,4,6,8 \} [/tex]


The intersection [tex] E \cap F [/tex] 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 [tex] E \cap F [/tex] 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


[tex] D \cap (E \cap F) = \{4\} [/tex]

DeanR

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


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