Question

build a venn diagram.

• use the names of the sets to label the regions.
• place the numbers in the correct regions.

names of the sets
integers
whole numbers
rational numbers
numbers
-28 33
-20 -8.41
0

Explanation:

Step1: Recall definitions

• Rational numbers: Numbers that can be written as $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b

eq0$. All integers are rational numbers.

• Integers: $\{\cdots,- 2,-1,0,1,2,\cdots\}$.
• Whole numbers: $\{0,1,2,3,\cdots\}$.

Step2: Classify each number

• For $-28$: It is an integer (since $-28\in\mathbb{Z}$) and a rational number (because $-28=\frac{-28}{1}$). But it is not a whole number (whole numbers are non - negative).
• For $-20$: It is an integer (since $-20\in\mathbb{Z}$) and a rational number (because $-20=\frac{-20}{1}$). But it is not a whole number.
• For $0$: It is a whole number (by definition), an integer (since $0\in\mathbb{Z}$), and a rational number (because $0 = \frac{0}{1}$).
• For $33$: It is a whole number (by definition), an integer (since $33\in\mathbb{Z}$), and a rational number (because $33=\frac{33}{1}$).
• For $-8.41$: It is a rational number (since $-8.41=\frac{-841}{100}$), but it is not an integer (because it has a non - zero decimal part).

Step3: Label the Venn diagram

• Label the inner circle as "Whole numbers". Place $0$ and $33$ in this circle.
• Label the outer circle (that contains the inner circle) as "Integers". Place $-28$ and $-20$ in the part of the "Integers" circle that is not in the "Whole numbers" circle.
• All the numbers ($-28,-20,0,33,-8.41$) are in the "Rational numbers" set (since the set of integers is a subset of rational numbers). Place $-8.41$ in the part of the "Rational numbers" region that is not in the "Integers" circle.

Answer:

• Inner circle (Whole numbers): $0,33$
• Part of the Integers circle (not in the Whole numbers circle): $-28,-20$
• Part of the Rational numbers region (not in the Integers circle): $-8.41$