Question

which venn diagram correctly describes the relationship between set q and set i? q = {rational numbers} i = {irrational numbers} a , because all rational numbers are irrational numbers b , because rational and irrational numbers have no elements in common c , because all irrational numbers are rational numbers d , because some rational numbers are not irrational numbers

Explanation:

Step1: Recall number - set definitions

Rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$. Irrational numbers cannot be written as a fraction of two integers.

Step2: Analyze set - intersection

Since a number cannot be both rational and irrational simultaneously, the intersection of the set of rational numbers ($Q$) and the set of irrational numbers ($I$) is the empty set $\varnothing$.

Step3: Determine Venn - diagram

In a Venn - diagram, two sets with an empty intersection are represented as non - overlapping circles.

Answer:

B. Two non - overlapping circles representing $Q$ and $I$, because rational and irrational numbers have no elements in common.