Diagram showing relationship between real number sytem

Your diagram first divides the real number system into the "rational numbers" and "irrational numbers". The set of "rational numbers" is then subdivided into the "Integers" which has the "whole numbers" as a subset which has the "natural numbers" as a subset. The question then asks "which of the following sets has only rational numbers that are integers?". The given sets are
A: {4, -2, 2.75}
B: {2, 8, 0.2}
C: {−2,43,25,16}\displaystyle \{-2, \frac{4}{3},\sqrt{25}, 16\}
D: {164,−6,2,49}\displaystyle \{\frac{16}{4}, -6, 2, \sqrt{49}\}.

You have B circled. That is incorrect because 0.2 is not an integer. A is also incorrect because 2.75 is not an integer. Although 25=5\displaystyle \sqrt{25}= 5 is an integer, 43\displaystyle \frac{4}{3} is not so C is incorrect. 164=4\displaystyle \frac{16}{4}= 4 is an integer and so is 49=7\displaystyle \sqrt{49}= 7, so D: {4, -6, 2, 7} is the correct answer.
 
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