Diagram showing relationship between real number sytem
- Thread starter BK1113
- Start date
pka
Elite Member
- Joined
- Jan 29, 2005
- Messages
- 11,971
OK, I have seen the attachment. What is your answer?
Note that the instructions say rational numbers that are also integers.
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
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: \(\displaystyle \{-2, \frac{4}{3},\sqrt{25}, 16\}\)
D: \(\displaystyle \{\frac{16}{4}, -6, 2, \sqrt{49}\}\).
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 \(\displaystyle \sqrt{25}= 5\) is an integer, \(\displaystyle \frac{4}{3}\) is not so C is incorrect. \(\displaystyle \frac{16}{4}= 4\) is an integer and so is \(\displaystyle \sqrt{49}= 7\), so D: {4, -6, 2, 7} is the correct answer.
A: {4, -2, 2.75}
B: {2, 8, 0.2}
C: \(\displaystyle \{-2, \frac{4}{3},\sqrt{25}, 16\}\)
D: \(\displaystyle \{\frac{16}{4}, -6, 2, \sqrt{49}\}\).
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 \(\displaystyle \sqrt{25}= 5\) is an integer, \(\displaystyle \frac{4}{3}\) is not so C is incorrect. \(\displaystyle \frac{16}{4}= 4\) is an integer and so is \(\displaystyle \sqrt{49}= 7\), so D: {4, -6, 2, 7} is the correct answer.