Provide an appropriate response.
-Which of the following sets: N, Z, Q and I, together compose the set of real numbers?
A) I and Z together
B) Z and Q together
C) N and Z together
D) I and Q together

Question

Quizplus · Accepted Answer

The set of real numbers includes all rational and irrational numbers. The set of rational numbers (Q) includes integers (Z) and fractions. The set of irrational numbers (I) includes numbers that cannot be expressed as a fraction. Therefore, the combination of the sets of rational and irrational numbers (Q and I) would be the set of real numbers. The set of real numbers includes all rational and irrational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers (e.g., 1/2, 3/4, 5/6), while irrational numbers cannot be expressed as a ratio of two integers (e.g., √2, √3, π). N (the set of natural numbers) only includes positive integers and does not include negative numbers or fractions, so it is not enough to compose the set of real numbers. Z (the set of integers) includes both positive and negative integers but does not include fractions or irrational numbers, so it is also not enough to compose the set of real numbers. Q (the set of rational numbers) includes all fractions but not all irrational numbers, so it is not enough to compose the set of real numbers. However, I (the set of irrational numbers) includes all irrational numbers and, when combined with the set of rational numbers (Q), forms the set of real numbers. Therefore, the best choice is D.

Provide an Appropriate Response