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
irrational numbers
rational numbers
whole numbers
numbers
-19\pi
\sqrt{6}
-68
\frac{9}{2}
0

Explanation:

Step1: Recall number - set definitions

Whole numbers are non - negative integers (0, 1, 2, ...). Integers are whole numbers and their negatives (...,-2, - 1, 0, 1, 2,...). 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.

Step2: Classify the numbers

• For $-19\pi$: Since $\pi$ is irrational, $-19\pi$ is irrational.
• For $\sqrt{6}$: It cannot be written as a fraction of two integers, so it is irrational.
• For $-68$: It is an integer. Also, since it can be written as $\frac{-68}{1}$, it is rational.
• For $0$: It is a whole number, an integer, and a rational number (since $0=\frac{0}{1}$).
• For $\frac{9}{2}$: It is a rational number.

Step3: Place numbers in Venn - diagram

• In the "Whole numbers" circle, place $0$.
• In the "Integers" circle (which includes whole numbers), place $-68$ and $0$.
• In the "Rational numbers" circle (which includes integers), place $-68$, $0$, $\frac{9}{2}$.
• In the "Irrational numbers" region (outside the rational - numbers circle), place $-19\pi$ and $\sqrt{6}$.

Answer:

The Venn - diagram has a large circle labeled "Rational numbers". Inside this circle, there is a smaller circle labeled "Integers", and inside the "Integers" circle, there is a smaller circle labeled "Whole numbers". Outside the "Rational numbers" circle is the region for "Irrational numbers". In the "Whole numbers" circle: $0$. In the "Integers" circle: $-68,0$. In the "Rational numbers" circle: $-68,0,\frac{9}{2}$. In the "Irrational numbers" region: $-19\pi,\sqrt{6}$.