Question

(a) use the names of the sets to label the regions of the venn diagram.
names of the sets
integers
irrational numbers
rational numbers
whole numbers
(b) true or false?

Explanation:

Step1: Recall Number Set Hierarchy

Whole numbers (e.g., \(0, 1, 2, \dots\)) are a subset of integers (e.g., \(\dots, -2, -1, 0, 1, 2, \dots\)). Integers are a subset of rational numbers (numbers expressible as \(\frac{a}{b}\), \(b
eq0\), \(a,b\in\mathbb{Z}\)). Rational and irrational numbers are disjoint and together form real numbers.

Step2: Label Innermost Circle

The smallest (innermost) circle should be "Whole numbers" (since whole numbers are a subset of integers).

Step3: Label Middle Circle

The middle (purple) circle, containing the innermost, is "Integers" (as integers include whole numbers).

Step4: Label Left Rectangle (Outside Middle Circle, Inside Large Rectangle)

The region inside the large left rectangle but outside the purple circle is "Rational numbers" (excluding integers, e.g., \(\frac{1}{2}\), \(-\frac{3}{4}\)).

Step5: Label Right Rectangle

The right rectangle (separate from the left) is "Irrational numbers" (numbers like \(\sqrt{2}\), \(\pi\), not expressible as \(\frac{a}{b}\)).

Answer:

• Innermost circle: Whole numbers
• Middle (purple) circle: Integers
• Left region (outside purple, inside left rectangle): Rational numbers
• Right rectangle: Irrational numbers