Question

1. which venn diagram correctly represents the relationship between rational numbers and irrational numbers?

a. venn diagram with two separate circles labeled rational numbers and irrational numbers inside a rectangle labeled real numbers because rational numbers and irrational numbers have no numbers in common
b. venn diagram with two overlapping circles labeled rational numbers and irrational numbers inside a rectangle labeled real numbers because some irrational numbers are also rational numbers
c. venn diagram with irrational numbers as a larger circle and rational numbers as a smaller circle inside it, all within real numbers because all rational numbers are also irrational numbers
d. venn diagram with rational numbers as a larger circle and irrational numbers as a smaller circle inside it, all within real numbers because all irrational numbers are also rational numbers

Explanation:

Rational numbers are numbers that can be written as $\frac{p}{q}$ where $p$ and $q$ are integers ($q
eq0$), while irrational numbers cannot be expressed in this form. These two sets have no overlapping elements, and together they make up all real numbers.

Answer:

A. Rational numbers and irrational numbers have no numbers in common (with the Venn diagram showing two separate circles inside the real numbers rectangle)